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Cartographers utilize primary and secondary colors in producing color maps. It is relatively easy to print the primary colors of magenta, cyan, and yellow on photo paper. It is considerably more difficult to print the secondary colors of red, blue, green, orange, purple, seagreen, and leafgreen consistently.This thesis has solved the problem associated with producing photographic color for cartographic maps. A new system of developing color maps has been developed. This system has produced: (1) pure blacks, (2) suitable secondary colors, (3) pastel colors, and (4) mid-value and dark colors.

Dating back to the 1930's, Ramsey theory still intrigues many who study combinatorics. Roughly put, it makes the profound assertion that complete disorder is impossible. One view of this problem is in edge-colorings of complete graphs. For forbidden graphs H1,...,Hk and a graph G, we write G "arrows" (H1,...,Hk) if every k-edge-coloring of G contains a monochromatic copy of Hi in color i for some i=1,2,...,k. If c is a (red, blue)-edge-coloring of G, we say c is a bad coloring if G contains no red K3or blue K1,t under c. A graph G is (H1,...,Hk)-Ramsey-minimal if G arrows (H1,...,Hk) but no proper subgraph of G has this property. Given a family F of graphs, we say that a graph G is F-saturated if no member of F is a subgraph of G, but for any edge xy not in E(G), G + xy contains a member of F as a subgraph. Letting Rmin(K3, K1,t) be the family of (K3,K1,t)-Ramsey minimal graphs, we study the saturation number, denoted sat(n,Rmin(K3,K1,t)), which is the minimum number of edges among all Rmin(K3,K1,t)-saturated graphs on n vertices. We believe the methods and constructions developed in this thesis will be useful in studying the saturation numbers of (K4,K1,t)-saturated graphs.

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京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第21770号 / 工博第4587号 / 新制||工||1715(附属図書館) / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 中村 裕一, 教授 小山田 耕二, 教授 喜多 一 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

SAMMANFATTNING  Syfte  Syftet med studien var att undersöka huruvida färginfiltrering med effektfärg påverkar böjhållfastheten i flerskiktad zirkonia.  Material och metod Zirkoniamaterialet KATANA™ Zirconia YML, Kuraray Noritake användes i studien. Totalt framställdes 54 stycken provkroppar varav sex stycken utgjorde en pilotstudie för polering. Resterande 48 delades in i sex grupper (n = 8). Tre av grupperna frästes ut från Emalj och Body 1 (E-B1) och de resterande tre grupperna frästes ut från Body 2 och Body 3 (B2-B3). Två grupper, från de olika skikten, infiltrerades med Esthetic Colorant A plus (A), två grupper infiltrerades med Esthetic Colorant Opaque (O) samt två grupper utgjorde kontrollgrupper utan infiltrering (K). Provkropparna infiltrerades och sintrades enligt fabrikantens anvisningar. Därefter polerades de enligt ett poleringsschema och slutligen genomfördes ett biaxialt böjhållfasthetstest. Resultaten från samtliga grupper analyserades med One-way ANOVA, Tukey’s test, med en signifikansnivå på α = 0,05 med hjälp av statistikprogrammet SPSS.  Resultat Resultatet påvisade ingen signifikant skillnad i böjhållfastheten inom grupperna för de två skikten (E-B1A, E-B1O och E-B1K) samt (B2-B3A, B2-B3O och B2-B3K). Grupperna med skikten som inkluderade B2-B3 uppvisade signifikant högre böjhållfasthet oavsett infiltrering/kontroll än grupperna E-B1A, E-B1O och E-B1K.   Slutsats Böjhållfastheten i flerskiktad zirkonia påverkas inte av infiltrering med effektfärg. / ABSTRACT Purpose The purpose of this in vitro study was to investigate whether color infiltration with effect colors affect the biaxial flexural strength of multilayer zirconia.   Material and method The zirconia material KATANA™ Zirconia YML, Kuraray Noritake was used in the study. A total of 54 specimens were produced, of which six were part of a pilot study for polishing. The remaining 48 were divided into six groups (n=8). Three of the groups were milled of Enamel and Body 1 (E-B1) and the remaining three groups were milled of Body 2 and Body 3 (B2-B3). Two groups, from the different layers, were colored with Esthetic Colorant A plus (A), two groups were colored with Esthetic Colorant Opaque (O), while two groups served as control groups (K). The specimens were colored and sintered according to the manufacturer's instructions, polished according to a polishing schedule, and finally a biaxial flexural strength test was performed. The results were analyzed using One-way ANOVA, Tukey's test, with a significance level of α = 0.05 using the statistical software SPSS.   Results The results showed no significant difference in flexural strength within the groups for the two layers (E-B1A, E-B1O, and E-B1K) and (B2-B3A, B2-B3O, and B2-B3K). The groups with layers that included B2-B3 showed significantly higher flexural strength regardless of coloring/control than the groups E-B1A, E-B1O, and E-B1K.  Conclusion The flexural strength of multilayered zirconia is not affected by color infiltration with effect colors.

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

In theoretical computer science, various notions of efficiency are used for algorithms. The most commonly used notion is worst-case efficiency, which is defined by requiring polynomial worst-case running time. Another commonly used notion is average-case efficiency for random inputs, which is roughly defined as having polynomial expected running time with respect to the random inputs. Depending on the actual notion of efficiency one uses, the approximability of a combinatorial optimization problem can be very different. In this dissertation, the approximability of three classical combinatorial optimization problems, namely Independent Set, Coloring, and Shortest Common Superstring, is investigated for different notions of efficiency. For the three problems, approximation algorithms are given, which guarantee approximation ratios that are unachievable by worst-case efficient algorithms under reasonable complexity-theoretic assumptions. The algorithms achieve polynomial expected running time for different models of random inputs. On the one hand, classical average-case analyses are performed, using totally random input models as the source of random inputs. On the other hand, probabilistic analyses are performed, using semi-random input models inspired by the so called smoothed analysis of algorithms. Finally, the expected performance of well known greedy algorithms for random inputs from the considered models is investigated. Also, the expected behavior of some properties of the random inputs themselves is considered.