A proper edge coloring of G =(V,E)is a map c : E → C (where C is the set of available colors ) with c(e) ≠ c(ƒ) for any adjacent edges e,f. The minimum number of colors needed to properly color the edges of G, is called the chromatic index of Gand is denoted by χ(G). A proper edge coloring c is called acyclic if there are no bichromatic cycles in the graph. In other words an edge coloring is acyclic if the union of any two color classes induces a set of paths (i.e., linear forest) in G. The acyclic edge chromatic number (also called acyclic chromatic index), denoted by a’(G), is the minimum number of colors required to acyclically edge color G. The primary motivation for this thesis is the following conjecture by Alon, Sudakov and Zaks [7] (and independently by Fiamcik [22]): Acyclic Edge Coloring Conjecture: For any graph G, a’ (G) ≤ Δ(G)+2. The following are the main results of the thesis: 1 From a result of Burnstein [16], it follows that any subcubic graph can be acyclically edge colored using at most 5 colors. Skulrattankulchai [38] gave a polynomial time algorithm to color a subcubic graph using Δ + 2 = 5 colors. We proved that any non-regular subcubic graph can be acyclically colored using only 4 colors. This result is tight. This also implies that the fifth color, when needed is required only for one edge. 2 Let G be a connected graph on n vertices, m ≤ 2n - 1 edges and maximum degree Δ ≤ 4, then a’ (G) ≤ 6. This implies that graph of maximum degree 4 are acyclically edge colorable using at most 7 colors. 3 The earliest result on acyclic edge coloring of 2-degenerate graphs was by Caro and Roditty [17], where they proved that a’ (G) ≤ Δ + k - 1, where k is the maximum edge connectivity, defined as k = maxu,vε V(G)λ(u,v), where λ(u,v)is the edge-connectivity of the pair u,v. Note that here k can be as high as Δ. Muthu,Narayanan and Subramanian [34] proved that a’ (G) ≤ Δ + 1for outerplanar graphs which are a subclass of 2-degenerate graphs and posed the problem of proving the conjecture for 2-degenerate graphs as an open problem. In fact they have also derived an upper bound of Δ+1 for series-parallel graphs [35], which is a slightly bigger subclass of 2-degenerate graphs. We proved that 2-degenerate graphs are Δ+1colorable. 1 Fiedorowicz, Hauszczak and Narayanan [24] gave an upper bound of 2Δ+29 for planar graphs. Independently Hou, Wu, GuiZhen Liu and Bin Liu [29] gave an upper bound of max(2Δ - 2,Δ+ 22). We improve this upper bound to Δ+12, which is the best known bound at present. 2 Fiedorowicz, Hauszczak and Narayanan [24] gave an upper bound of Δ+6for triangle free planar graphs. We improve the bound to Δ+3, which is the best known bound at present. 3 We have also worked on lower bounds. Alon et.al. [7], along with the acyclic edge coloring conjecture, also made an auxiliary conjecture stating that Complete graphs of 2n vertices are the only class of regular graphs which require Δ+2colors. We disproved this conjecture by showing infinite classes of regular graphs other than Complete Graphs which require Δ+2colors. Apart from the above mentioned results, this thesis also contributes to the acyclic edge coloring literature by introducing new techniques like Recoloring, Color Exchange (exchanging colors of adjacent edges), circular shifting of colors on adjacent edges (derangement of colors). These techniques turn out to be very useful in proving upper bounds on the acyclic edge chromatic number.

La thèse porte sur les deux thèmes des Jeux combinatoires et de la théorie des graphes. Elle est divisée en deux parties.1) Le jeu de Domination et ses variantes: Il s'agit d'un jeu combinatoire qui consiste à marquer les sommets d'un graphe de telle sorte qu'un sommet marqué n'ait aucun voisin marqué. Le joueur marquant le dernier sommet est déclaré gagnant. Le calcul des stratégies gagnantes étant NP-difficile pour un graphe quelconque, nous avons étudié des familles particulières de graphes comme les chemins, les scies ou les chenilles. Pour ces familles on peut savoir en temps polynomial si un graphe est perdant. Nous avons également étudié 28 variantes du jeu de domination, dont les 12 variantes définies par J. Conway sur un jeu combinatoire quelconque. 2) Le nombre chromatique ludique des arbres: Ce paramètre est calculé à partir d'un jeu de coloration où Alice et Bob colorient alternativement et proprement un sommet d'un graphe G avec l'une des k couleurs. L'objectif d'Alice est de colorier complètement le graphe alors que Bob doit l'en empêcher. Nous nous sommes intéressés au jeu avec 3 couleurs sur un arbre T. Nous souhaitons déterminer les arbres ayant un nombre chromatique ludique 3, soit ceux pour lesquels Alice a une stratégie gagnante avec 3 couleurs. Ce problème semblant difficile à résoudre sur les arbres, nous avons résolu des sous-familles: les 1-chenilles puis les chenilles sans trous. / Part 1: Domination Game and its variantsDomination game is a combinatorial game that consists in marking vertices of a graph so that a marked vertex has no marked neighbors. The first player unable to mark a vertex loses the game.Since the computing of winning strategies is an NP-hard problem for any graphs, we examine some specific families of graphs such as complete k-partite graphs, paths or saws. For these families, we establish the set of losing elements. For other families, such as caterpillars, we prove that exists a polynomial algorithm for the computation of outcome and winning strategies. No polynomial algorithm has been found to date for more general families, such as trees.We also study 28 variants of Domination game, including the 12 variants defined by J. Conway for any combinatorial game. Using game functions, we find the set of losing paths for 10 of these 12 variants. We also investigate 16 variants called diameter, for instance when rules require to play on the component that has the largest diameter.Part 2: The game chromatic number of treesThis parameter is computed from a coloring game: Alice and Bob alternatively color the vertices of a graph G, using one of the k colors in the color set. Alice has to achieve the coloring of the entire graph whereas Bob has to prevent this. Faigle and al. proved that the game chromatic number of a tree is at most 4. We undertake characterization of trees with a game chromatic number of 3. Since this problem seems difficult for general trees, we focus on sub-families: 1-caterpillars and caterpillars without holes.For these families we provide the characterization and also compute winning strategies for Alice and Bob. In order to do so, we are led to define a new notion, the bitype, that for a partially-colored graph G associates two letters indicating who has a winning strategy respectively on G and G with an isolated vertex. Bitypes allow us to demonstrate several properties, in particular to compute the game chromatic number of a graph from the bitypes of its connected components.

Dans un graphe non orienté, le Problème de Coloration de Graphe (PCG) consiste à assigner à chaque sommet du graphe une couleur de telle sorte qu'aucune paire de sommets adjacents n'aient la même couleur et le nombre total de couleurs est minimisé. DSATUR est un algorithme exact efficace pour résoudre le PCG. Un de ses défauts est qu'une borne inférieure est calculée une seule fois au noeud racine de l'algorithme de branchement, et n'est jamais mise à jour. Notre nouvelle version de DSATUR surpasse l'état de l'art pour un ensemble d'instances aléatoires à haute densité, augmentant significativement la taille des instances résolues. Nous étudions trois formulations PLNE pour le Problème de la Somme Chromatique Minimale (PSCM). Chaque couleur est représentée par un entier naturel. Le PSCM cherche à minimiser la somme des cardinalités des sous-ensembles des sommets recevant la même couleur, pondérés par l'entier correspondant à la couleur, de telle sorte que toute paire de sommets adjacents reçoive des couleurs différentes. Nous nous concentrons sur l'étude d'une formulation étendue et proposons un algorithme de Branch-and-Price. / Given an undirected graph, the Vertex Coloring Problem (VCP) consists of assigning a color to each vertex of the graph such that two adjacent vertices do not share the same color and the total number of colors is minimized. DSATUR is an effective exact algorithm for the VCP. We introduce new lower bounding techniques enabling the computing of a lower bound at each node of the branching scheme. Our new DSATUR outperforms the state of the art for random VCP instances with high density, significantly increasing the size of solvable instances. Similar results can be achieved for a subset of high density DIMACS instances. We study three ILP formulations for the Minimum Sum Coloring Problem (MSCP). The problem is an extension of the classical Vertex Coloring Problem in which each color is represented by a positive natural number. The MSCP asks to minimize the sum of the cardinality of subsets of vertices receiving the same color, weighted by the index of the color, while ensuring that vertices linked by an edge receive different colors. We focus on studying an extended formulation and devise a complete Branch-and-Price algorithm.

Les deux problèmes majeurs considérés dans cette thèse : le b-coloration problème et le graphe emballage problème. 1. Le b-coloration problème : Une coloration des sommets de G s'appelle une b-coloration si chaque classe de couleur contient au moins un sommet qui a un voisin dans toutes les autres classes de couleur. Le nombre b-chromatique b(G) de G est le plus grand entier k pour lequel G a une b-coloration avec k couleurs. EL Sahili et Kouider demandent s'il est vrai que chaque graphe d-régulier G avec le périmètre au moins 5 satisfait b(G) = d + 1. Blidia, Maffray et Zemir ont montré que la conjecture d'El Sahili et de Kouider est vraie pour d ≤ 6. En outre, la question a été résolue pour les graphes d-réguliers dans des conditions supplémentaires. Nous étudions la conjecture d'El Sahili et de Kouider en déterminant quand elle est possible et dans quelles conditions supplémentaires elle est vrai. Nous montrons que b(G) = d + 1 si G est un graphe d-régulier qui ne contient pas un cycle d'ordre 4 ni d'ordre 6. En outre, nous fournissons des conditions sur les sommets d'un graphe d-régulier G sans le cycle d'ordre 4 de sorte que b(G) = d + 1. Cabello et Jakovac ont prouvé si v(G) ≥ 2d3 - d2 + d, puis b(G) = d + 1, où G est un graphe d-régulier. Nous améliorons ce résultat en montrant que si v(G) ≥ 2d3 - 2d2 + 2d alors b(G) = d + 1 pour un graphe d-régulier G. 2. Emballage de graphe problème : Soit G un graphe d'ordre n. Considérer une permutation σ : V (G) → V (Kn), la fonction σ* : E(G) → E(Kn) telle que σ *(xy) = σ *(x) σ *(y) est la fonction induite par σ. Nous disons qu'il y a un emballage de k copies de G (dans le graphe complet Kn) s'il existe k permutations σi : V (G) → V (Kn), où i = 1, …, k, telles que σi*(E(G)) ∩ σj (E(G)) = ɸ pour i ≠ j. Un emballage de k copies d'un graphe G est appelé un k-placement de G. La puissance k d'un graphe G, noté par Gk, est un graphe avec le même ensemble de sommets que G et une arête entre deux sommets si et seulement si le distance entre ces deux sommets est au plus k. Kheddouci et al. ont prouvé que pour un arbre non-étoile T, il existe un 2-placement σ sur V (T). Nous introduisons pour la première fois le problème emballage marqué de graphe dans son graphe puissance / Two problems are considered in this thesis: the b-coloring problem and the graph packing problem. 1. The b-Coloring Problem : A b-coloring of a graph G is a proper coloring of the vertices of G such that there exists a vertex in each color class joined to at least a vertex in each other color class. The b-chromatic number of a graph G, denoted by b(G), is the maximum number t such that G admits a b-coloring with t colors. El Sahili and Kouider asked whether it is true that every d-regular graph G with girth at least 5 satisfies b(G) = d + 1. Blidia, Maffray and Zemir proved that the conjecture is true for d ≤ 6. Also, the question was solved for d-regular graphs with supplementary conditions. We study El Sahili and Kouider conjecture by determining when it is possible and under what supplementary conditions it is true. We prove that b(G) = d+1 if G is a d-regular graph containing neither a cycle of order 4 nor of order 6. Then, we provide specific conditions on the vertices of a d-regular graph G with no cycle of order 4 so that b(G) = d + 1. Cabello and Jakovac proved that if v(G) ≥ 2d3 - d2 + d, then b(G) = d + 1, where G is a d-regular graph. We improve this bound by proving that if v(G) ≥ 2d3 - 2d2 + 2d, then b(G) = d+1 for a d-regular graph G. 2. Graph Packing Problem : Graph packing problem is a classical problem in graph theory and has been extensively studied since the early 70's. Consider a permutation σ : V (G) → V (Kn), the function σ* : E(G) → E(Kn) such that σ *(xy) = σ *(x) σ *(y) is the function induced by σ. We say that there is a packing of k copies of G into the complete graph Kn if there exist k permutations σ i : V (G) → V (Kn), where i = 1,…, k, such that σ*i (E(G)) ∩ σ*j (E(G)) = ɸ for I ≠ j. A packing of k copies of a graph G will be called a k-placement of G. The kth power Gk of a graph G is the supergraph of G formed by adding an edge between all pairs of vertices of G with distance at most k. Kheddouci et al. proved that for any non-star tree T there exists a 2-placement σ on V (T). We introduce a new variant of graph packing problem, called the labeled packing of a graph into its power graph

Les applications réelles liées aux problèmes de satisfaction partielle de contraintes (PCSP : Partial Constraints Satisfaction Problem) sont de plus en plus nombreuses, ce qui justifie l’intérêt croissant des chercheurs pour cette classe de problèmes. La résolution d’un PCSP revient à affecter des valeurs à toutes ses variables tout en maximisant (ou minimisant) une fonction objectif prédéfinie. Ces problèmes sont NP-difficiles, par conséquent il n’existe aucune approche aussi bien exacte qu’heuristique efficace sur les grandes instances. Pour résoudre efficacement les instances difficiles, une multitude de solutions sont proposées, allant de l’hybridation à l’apprentissage en passant par la décomposition. Dans notre travail, nous nous intéressons à cette dernière proposition, qui consiste à fractionner le problème PCSP en plusieurs sous-problèmes PCSP de tailles raisonnables, puis proposer des algorithmes de résolution pour les problèmes décomposés. Cette approche a pour but de bénéficier de la structure du problème afin d’accélérer sa résolution tout en garantissant des solutions optimales ou sous-optimales. Deux grand axes sont explorés : les approches basées sur la décomposition et celles guidées par la décomposition. Les approches basées sur la décomposition consistent à résoudre séparément les parties difficiles du problème décomposé, puis combiner les solutions partielles obtenues en vue d’atteindre une solution globale du problème d’origine. Les approches guidées par la décomposition consistent à développer des métaheuristiques qui tiennent compte de la structure du problème décomposé. Les algorithmes proposés sont testés et validés sur des instances réelles des problèmes PSCP, comme le problème d’affectation de fréquences et le problème de coloration de graphes / The wide range of potential applications concerned by the resolution of Partial Constraints Satisfaction Problems (PCSP) justifies the growing interest of scientists in this class of problems. Solving a PCSP means searching for values to assign to the decision variables in order to maximize (or minimize) a predefined objective function. These problems are NP-hard, so there isn’t an exact approach nor an efficient heuristic able to provide the optimal solution for large instances. In order to solve effectively the difficult instances, numerous approaches based on hybridization, learning or decomposition are proposed. In the present work, we focus on the latter proposal, which consists in splitting the PCSP into several smaller size PCSPs and we propose some methods to solve the decomposed problem. Two wide axes are explored : the resolution based on the decomposition and the one guided by decomposition. The former solves separately the difficult parts of the decomposed problem (cuts or clusters) and then combines partial solutions obtained in order to achieve a global solution for the original problem. The latter aims at benefiting from the structure of the problem to be decomposed in order to accelerate its resolution while ensuring optimal or near optimal solutions. All the proposed algorithms are tested and validated on the well-known benchmarks of PCSP problems such as Frequency Assignment Problem (FAP) and graph coloring problem

The vertex coloring problem is a classic problem in graph theory that asks for a partition of the vertex set into a minimum number of stable sets. This thesis presents our studies on three vertex (re)coloring problems on graphs and on a problem related to a long-standing conjecture on subdivision of digraphs. Firstly, we address the convex recoloring problem in which an arbitrarily colored graph G is given and one wishes to find a minimum weight recoloring such that each color class induces a connected subgraph of G. We show inapproximability results, introduce an integer linear programming (ILP) formulation that models the problem and present some computational experiments using a column generation approach. The k-fold coloring problem is a generalization of the classic vertex coloring problem and consists in covering the vertex set of a graph by a minimum number of stable sets in such a way that every vertex is covered by at least k (possibly identical) stable sets. We present an ILP formulation for this problem and show a detailed polyhedral study of the polytope associated with this formulation. The last coloring problem studied in this thesis is the proper orientation problem. It consists in orienting the edge set of a given graph so that adjacent vertices have different in-degrees and the maximum in-degree is minimized. Clearly, the in-degrees induce a partition of the vertex set into stable sets, that is, a coloring (in the conventional sense) of the vertices. Our contributions in this problem are on hardness and upper bounds for bipartite graphs. Finally, we study a problem related to a conjecture of Mader from the eighties on subdivision of digraphs. This conjecture states that, for every acyclic digraph H, there exists an integer f(H) such that every digraph with minimum out-degree at least f(H) contains a subdivision of H as a subdigraph. We show evidences for this conjecture by proving that it holds for some particular classes of acyclic digraphs. / O problema de coloração de grafos é um problema clássico em teoria dos grafos cujo objetivo é particionar o conjunto de vértices em um número mínimo de conjuntos estáveis. Nesta tese apresentamos nossas contribuições sobre três problemas de coloração de grafos e um problema relacionado a uma antiga conjectura sobre subdivisão de digrafos. Primeiramente, abordamos o problema de recoloração convexa no qual é dado um grafo arbitrariamente colorido G e deseja-se encontrar uma recoloração de peso mínimo tal que cada classe de cor induza um subgrafo conexo de G. Mostramos resultados sobre inaproximabilidade, introduzimos uma formulação linear inteira que modela esse problema, e apresentamos alguns resultados computacionais usando uma abordagem de geração de colunas. O problema de k-upla coloração é uma generalização do problema clássico de coloração de vértices e consiste em cobrir o conjunto de vértices de um grafo com uma quantidade mínima de conjuntos estáveis de tal forma que cada vértice seja coberto por pelo menos k conjuntos estáveis (possivelmente idênticos). Apresentamos uma formulação linear inteira para esse problema e fazemos um estudo detalhado do politopo associado a essa formulação. O último problema de coloração estudado nesta tese é o problema de orientação própria. Ele consiste em orientar o conjunto de arestas de um dado grafo de tal forma que vértices adjacentes possuam graus de entrada distintos e o maior grau de entrada seja minimizado. Claramente, os graus de entrada induzem uma partição do conjunto de vértices em conjuntos estáveis, ou seja, induzem uma coloração (no sentido convencional) dos vértices. Nossas contribuições nesse problema são em complexidade computacional e limitantes superiores para grafos bipartidos. Finalmente, estudamos um problema relacionado a uma conjectura de Mader, dos anos oitenta, sobre subdivisão de digrafos. Esta conjectura afirma que, para cada digrafo acíclico H, existe um inteiro f(H) tal que todo digrafo com grau mínimo de saída pelo menos f(H) contém uma subdivisão de H como subdigrafo. Damos evidências para essa conjectura mostrando que ela é válida para classes particulares de digrafos acíclicos.

Nous étudions plusieurs problèmes de coloration dans les graphes, pour certains avec une composante ludique. La coloration à distance 2 d'un graphe est une coloration de ses sommets telle que deux sommets à distance au plus 2 ont des couleurs différentes. Le L(p; q)-étiquetage est une généralisation de ce problème ou les contraintes à distance 1 et 2 sont différentes. Nous donnons des résultats pour ces deux problèmes dans plusieurs classes de graphes peu denses (ayant un faible degré moyen maximum).Le jeu de coloration sur un graphe est un jeu ou deux joueurs, Alice et Bob, colorent tour à tour un des sommets non coloriés d'un graphe, construisant ainsi une coloration propre partielle de plus en plus étendue de ce graphe. Alice tente d'étendre la coloration à l'ensemble du graphe, et Bob tente de l'en empêcher. Nous travaillons sur un invariant de graphe, le degré minmax, dont l'étude permet de déduire des résultats pour le jeu de coloration via l'étude d'un problème structurel, la (1; k)-décomposition d'un graphe, c'est-à-dire la partition de ses arêtes en une forêt et un sous-graphe de degré inférieur ou égal à k.Nous travaillons enfin sur une variante du jeu de coloration nommée jeu de coloration d'incidences, ou Alice et Bob colorient les incidences d'un graphe, pour lequel nous donnons une stratégie efficace pour Alice.Enfin, tout au long de notre mémoire, nous étudions les liens entre la notion de coloration est celle de marquage. Un marquage est un ordre sur les sommets (ou arêtes, ou incidences...) d'un graphe possédant des caractéristiques utiles pour le colorer. Pour nos différents problèmes, nous questionnons l'utilité ou les limites de l'usage de cette notion. / We study several problems of graph coloring, some of them with a game component.A 2-distance coloring of a graph is a vertex coloring where two vertices at distanceat most two have different colors. A L(p; q)-labeling is a generalisation of the distance-2coloring where constraints are different at distance 1 and 2. We give results for thesetwo problems in several classes of sparse graphs (with a low maximal average degree).The coloring game on a graph is a game where two players, Alice and Bob, taketurns coloring an uncolored vertex of the graph, constructing together a proper partialcoloring of the graph extending as time moves on. Alice try to extend the coloringto the whole graph, and Bob try to prevent her to win. We study a graph invariant,the minmax degree, who has consequences on the coloring game through the notion of(1; k)-decomposition of a graph, which is the partition of its edge set into a forest and asubgraph of degree bounded by k.We finally study a variant of the coloring game named incidence coloring game, whereAlice and Bob are coloring the incidences of a graph, and for which we give an efficientstrategy for Alice.Finally, during our thesis, we study the connections between coloring and marking,which is an order on the vertices of a graph (or its edges, or its incidences) havingproperties usefull for its coloring. For our problems, we try to determine the utility andthe limits of a marking-based approach of coloring problems.

著色問題(graph coloring problem)的研究已行之有年，並衍生出廣泛的實際應用，但還缺乏一般化的著色問題模型。本論文建構一般化的著色問題模型，其目標函數包含顏色成本的固定支出和點著色變動成本。此著色模型為0/1整數線性規畫模型，其限制式含有選點問題(node packing problem)的限制式。我們利用圖中的極大團(maximal clique)所構成的強力限制式，取代原有的選點限制式，縮短求解時間。我們更進一步舉出一個特殊指派問題並將此著色模型應用於此指派問題上。本論文亦針對此指派問題發展了一個演算法來尋找極大團。計算結果顯示極大團限制式對於此著色問題模型的求解有極大的效益。 / The graph coloring problem (GCP) has been studied for a long time and it has a wide variety of applications. A straightforward formulation of graph coloring problem has not been formulated yet. In this paper, we formulate a general GCP model that concerns setup cost and variable cost of different colors. The resulting model is an integer program that involves the packing constraint. The packing constraint in the GCP model can be replaced by the maximal clique constraint in order to shorten the solution time. A special assignment problem is presented which essentially is a GCP model application. An algorithm of finding maximal cliques for this assignment problem is developed. The computational results show the efficiency of maximal clique constraints for the GCP problem.

Modern embedded processors with dedicated address generation unit support memory accesses using indirect addressing mode with auto-increment and auto-decrement. The auto-increment/decrement mode, if properly utilized, can save address arithmetic instructions, reduce static and dynamic footprint of the program and speed up the execution as well. We propose an optimization framework for embedded processors based on the auto-increment and decrement addressing modes for address registers. Existing work on this class of optimizations focuses on using an access graph and finding the maximum weight path cover to find an optimized stack variables layout. We take this further by using coalescing, addressing mode selection and offset registers to find further opportunities for reducing the number of load-address instructions required. We also propose an algorithm for building the layout with considerations for memory accesses across basic blocks, because existing work mainly considers intra-basic-block information. We then use the available offset registers to try to further reduce the number of address arithmetic instructions after layout assignment.

Les graphes sont des structures mathématiques utilisées pour modéliser les relations par paires entre objets. Malgré leur structure simple, les graphes ont des applications dans divers domaines tels que l'informatique, la physique, la biologie et la sociologie. L'objectif principal de ce travail est de continuer l'étude des problèmes de coloration et de détection dans le cadre de classes de graphes fermées par sous-graphes induits (que nous appelons classes de graphes héréditaires).La première classe que nous considérons est graphes sans ISK4 - les graphes qui ne contiennent aucune subdivision de en tant que sous-graphe induit. Nous montrons que le nombre chromatique de cette classe est limité à 24, une amélioration considérable par rapport à la borne existant précédemment. Nous donnons également une bien meilleure limite dans le cas sans triangle. De plus, nous prouvons qu'il existe un algorithme de complexité pour détecter cette classe, ce qui répond à une question de Chudnovsky et al. et Lévêque et al.La deuxième classe que nous étudions est celle des graphes sans trou pair et sans étoile d’articulation. Cela est motivé par l'utilisation de la technique de décomposition pour résoudre certains problèmes d'optimisation. Nous garantissons la fonction χ-bounding optimale pour cette classe. Nous montrons que la classe a rank-width bornée, ce qui implique l'existence d'un algorithme de coloration en temps polynomial. Enfin, la coloration gloutonne connexe dans les graphes sans griffes est considérée. Une façon naturelle de colorier un graphe est d'avoir un ordre de ses sommets et d'affecter pour chaque sommet la première couleur disponible. Beaucoup de recherches ont été faites pour des ordres généraux. Cependant, nous connaissons très peu de choses sur la caractérisation des bons graphes par rapport aux ordres connexes. Un graphe est bon si pour chaque sous-graphe induit connexe de , chaque ordre connexe donne à une coloration optimale. Nous donnons la caractérisation complète de bons graphes sans griffes en termes de sous-graphes induits minimaux interdits. / Graphs are mathematical structures used to model pairwise relations between objects. Despite their simple structures, graphs have applications in various areas like computer science, physics, biology and sociology. The main focus of this work is to continue the study of the coloring and detecting problems in the setting of graph classes closed under taking induced subgraphs (which we call hereditary graph classes). The first class we consider is ISK4-free graphs - the graphs that do not contain any subdivision of K4 as an induced subgraph. We prove that the chromatic number of this class is bounded by 24, a huge improvement compared to the best-known bound. We also give a much better bound in the triangle-free case. Furthermore, we prove that there exists an O(n 9) algorithm for detecting this class, which answers a question by Chudnovsky et al. and Lévêque et al. The second class we study is even-hole-free graphs with no star cutset. This was motivated by the use of decomposition technique in solving some optimization problems. We prove the optimal χ -bounding function for this class and show that it has bounded rank-width, which implies the existence of a polynomial-time coloring algorithm.Finally, the connected greedy coloring in claw-free graphs is considered. A natural way to color a graph is to have an order of its vertices and assign for each vertex the first available color. A lot of researches have been done for general orders. However, we know very little about the characterization of good graphs with respect to connected orders. A graph G is good if for every connected induced subgraph H of G, every connected order gives H an optimal coloring. We give the complete characterization of good claw-free graphs in terms of minimal forbidden induced subgraphs.