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Detour Domination in GraphsChartrand, Gary, Haynes, Teresa W., Henning, Michael A., Zhang, Ping 01 April 2004 (has links)
For distinct vertices u and v of a nontrivial connected graph G, the detour distance D(u, v) between u and v is the length of a longest u-v path in G. For a vertex v ∈ V(G), define D-(v) = min{D(u, v) : u ∈ V(G) - {v}}. A vertex u (≠ v) is called a detour neighbor of v if D(u, v) = D -(v). A vertex u is said to detour dominate a vertex u if u = v or u is a detour neighbor of v. A set S of vertices of G is called a detour dominating set if every vertex of G is detour dominated by some vertex in S. A detour dominating set of G of minimum cardinality is a minimum detour dominating set and this cardinality is the detour domination number γD(G) . We show that if G is a connected graph of order n ≥ 3, then γD(G) ≤ n - 2. Moreover, for every pair k, n of integers with 1 ≤ k ≤ n - 2, there exists a connected graph G of order n such that γD(G) = k. It is also shown that for each pair a, b of positive integers, there is a connected graph G with domination number γ(G) = a and γD(G) = b.
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Hamiltonian Domination in GraphsChartrand, Gary, Haynes, Teresa W., Henning, Michael A., Zhang, Ping 01 November 2004 (has links)
For distinct vertices u and ν of a nontrivial connected graph G, the detour distance D(u, ν) between u and ν is the length of a longest u-ν path in C. For a vertex ν in G, define D+(ν) = max{D(u, ν) : u ∈ V(G) - {ν}}. A vertex u is called a hamiltonian neighbor of ν if D(u, ν) -D+(ν). A vertex v is said to hamiltonian dominate a vertex u if u = ν or u is a hamiltonian neighbor of ν. A set 5 of vertices of G is called a hamiltonian dominating set if every vertex of G is hamiltonian dominated by some vertex in S. A hamiltonian dominating set of minimum cardinality is a minimum hamiltonian dominating set and this cardinality is the hamiltonian domination number γH(G) of G. It is shown that if T is a tree of order n ≥ 3 and p is the order of the periphery of T, then γH(T) = n - p. It is also shown that if G is a connected graph of order n ≥ 3, then γH(G) ≤ n - 2. Moreover, for every pair k, n of integers with 1 ≤ k ≤ n - 2, there exists a connected graph G of order n such that γH(G) = k. For a vertex ν in G, define D- (ν) -min{D(u, ν) : u ∈ V(G) -{ν}}. A vertex u is called a detour neighbor of ν if D(u, ν) = D- (ν). The detour domination number γD(G) of G is defined analogously to γH(G)- It is shown that every pair a, b of positive integers is realizable as the domination number and hamiltonian domination number, respectively, of some graph. For integers a, b ≥ 2, the corresponding result is shown for the detour domination number and hamiltonian domination number. The problem of determining those rational numbers r and s with 0 < r, s < 1 for which there exists a graph G of order n such that γD(G)/n = r and γH/(G)/n = s is discussed.
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Application of a strategic learning approach and cognitive assessment of readiness for training in a criminal rehabilitation contextRoss, Virginia Hasler 11 February 2015 (has links)
One purpose of this research was to investigate whether a cognitive approach developed for business and industry could be usefully added to other measures in the assessment of recently incarcerated criminal trainees' readiness to benefit from and progress in a cognitive skills training program titled 'Dignity, Encouragement, Truthfulness, Optimism, Uniqueness, Respect' (DETOUR). Another important purpose of this study was to obtain data relevant to the role of strategic learning and, in particular, to Weinstein's Model of Strategic Leaming (1994), and to related conceptualizations such as Salomon and Perkins' suggestions about the teaching of thinking skills (1987). Eighty volunteer inmates housed in a state prison transfer facility, selected by the prison school district staff to participate in the DETOUR program, comprised the subject pool. Although participants were not randomly assigned for this study, they were representative of the state prison system population in age, IQ, grade equivalency, and length of sentence. Participants were pre- and post-tested on three self-report instruments, two of which were cognitive, the START and the Criminal Sentiments Scale (CSS), and one behavioral instrument, the Client Behavior Report (CBR), and several other measures available from the DETOUR program. Multiple regression analysis revealed that the START, when added to the independent variables age, IQ, grade equivalency, and number of times incarcerated, increased the adjusted variance predicted by these independent variables from 4.7% to 23.9% on the CSS outcome measure, a statistically significant increase. Within subjects T-tests revealed that the DETOUR program significantly and positively affected students' scores on all three instruments. Also, a large number of significant relationships among sub-scales of these instruments appeared to be of theoretical and practical interest. The results of this study substantiate the usefulness of a cognitive strategies approach to assessing inmates in a state prison training environment, and support the START instrument's convergent validity (Campbell, 1996). Results of this study also were consistent with components of Weinstein's Model of Strategic Leaming and Salomon and Perkins' high road/low road model of transfer. / text
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Route switching behavior among Austin commutersMotamed, Moggan 03 February 2014 (has links)
IH-35 is a major north-south interstate highway across the State of Texas. It is an
important business corridor, conveniently connecting four large Texas cities, Austin,
Dallas, Fort Worth, and San Antonio, as well as facilitating trade between Mexico and
the United States.
During construction of the SH-71/IH-35 Interchange, the Austin District of the
Texas Department of Transportation (TxDOT) has had to close the main lanes of IH-35
and re-route traffic. Three main lane closures happened during three weekends in 2011.
During those closures, a parallel route, the SH-130 toll road, was made free to travelers.
TxDOT provided both pre-trip and en-route information about the closure. They used
radio, TV, portable message sign (PMS), and dynamic message signs (DMS) to inform
commuters about the closure. To inform travelers passing through Austin about the
closure and the existing alternative (SH-130 was toll free), they even collaborated with
Dallas and San Antonio TxDOT district personnel.
However, usage of SH130 was less than anticipated, and there was significant
traffic queuing on IH-35. In this study, we tried to document the quantity of traffic that
used the alternative path during the IH-35 closure and explore options for relieving
delays on IH-35 during future closures. / text
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A (des)ordem doméstica : disposições, desvios e diálogosMonsell, Alice Jean January 2009 (has links)
A pesquisa de Doutorado em Poéticas Visuais, intitulada “A (des)ordem doméstica: Disposições, desvios e diálogos”, do PPGAV/IA/UFRGS, orientada pelo Prof. Dr. Hélio Fervenza desde 2005, partiu da visita a casas de colaboradoras, que registraram a disposição e o display dos objetos de seu lar. Na minha casa, comecei a desenvolver procedimentos táticos de détournement (desvio) das minhas práticas domésticas e artísticas com base em modelos da vida cotidiana – os registros das visitas, os processos domésticos materiais e sociais, sua efemeridade e seus acasos – notando algumas referências na arte: os Tableaux Piéges (Pinturas Armadilhas, 1960-70) de Daniel Spoerri. Gartenskulptur (1968- 96) de Dieter Roth, Gordon Matta-Clark, Kurt Schwitters, bem como a noção de “arte comoa- vida” em Allan Kaprow. Entre 2005 e 2006, emergem procedimentos de desvio (détournement) de processos de uso e da função de objetos domésticos a pa rtir de sua reconstrução, usando como materiais de trabalho as “sobras, que se referem aos objetos inúteis, guardados e acumulados na minha casa. A operação poética, a “to-pó-grafia”, investiga a disposição pelo desvio de um guardanapo de crochê para a função de matrizestêncil coberta com poeira, embaralhando a ordem cultural deste objeto. O gesto doméstico de varrer sofre o desvio através dos “re-enquadramentos”, quando poeira e detritos do chão são transformados em “quadros” pendurados na parede em cima do sofá, problematizando um modelo da arte, bem como um modelo doméstico de disposição e de display. A partir do final de 2006, experimentei com a inserção da documentação fotográfica das visitas em objetos domésticos reais ou reconstruídos. Esse é um dos procedimentos que elabora questões de apresentação pública. Emerge nesta etapa, a proposta de apresentação e display: a domesticação. Essa se refere à operação de “domesticar um espaço não-doméstico”, pela recontextualização. Por exemplo, de uma garagem, uma sala de aula ou galeria, a partir de modelos de disposição observados em casas. A domesticação de uma galeria faz com que a função estética dos objetos e sua função social oscilem, transformando o espaço em meio para fornecer um contexto para diálogo e trocas. Uma das táticas para potencializar tais interações inclui minha presença no espaço de apresentação, em certos dias e horários, para “receber as visitas”, trocar palavras, compartilhar chá com bolachas... visando a instaurar dúvidas sobre a função e a (des)ordem dos objetos ali dispostos e propor outro modelo social para as relações que podem ocorrer dentro de um espaço íntimo público. / The doctoral research project in Visual Poetics, entitled, “Domestic (dis)order: (dis)placements, detours and dialogues”, at the PPGAV/IA/UFRGS, oriented by Professor Hélio Fervenza, PhD since 2005, initially proposed visiting the houses of collaborators who recorded the placement and display of objects in their homes. In my house, I proceeded to develop tactical procedures of détournement (detour) of my domestic and artistic practices based on quotidian models - the records of visits and observed domestic material and social processes, both ephemeral and random - noting some of my references in art: the “Tableaux Piéges” (Snare Pictures) (1960-70) by Daniel Spoerri; “Gartenskulptur” (1968-96) by Dieter Roth; Gordon Matta-Clark, Kurt Schwitters, as well as the notion of “lifelike art” in Allan Kaprow. Between 2005 and 2006, procedures emerge that detour (deturn) the processes of use and the function of domestic objects through their reconstruction, using as work materials the “leftovers”, which refers to all useless objects that had been stored and were accumulating in my home. The “dust-o-graph” investigates the placement of crochet doilies by detouring their everyday function into a graphic tool for stenciling with household dust, shuffling this object’s cultural order. The household gesture of sweeping suffers a detour through the procedure of “re-picturing” when floor dust and scraps are transformed into “pictures” placed hanging on the wall above the sofa, problematizing a model of art, as well as a model of placement and display in the home. Toward the end of 2006, I began to experiment with insertion of photographic documents from visits into real or reconstructed domestic objects. This is one of the procedures developed to elaborate questions involving public presentation. At this stage, the poetic proposal of public presentation and display “domestication” emerges. This refers to the operation of “domesticating a non-domestic space” by recontextualizing, for example, an art gallery, a classroom or a garage using placement models observed in homes. The “domestication” of a gallery makes the aesthetic function of objects and its social order oscillate, transforming the space into a means to offer a context for dialogue and exchanges. One of the tactics for potentializing interactions is my own presence in the presentation space, at certain times, when I “receive visitors”, converse, offer tea and cookies… aiming to place doubt on the function and order of objects (dis)placed there and at proposing an alternative social model for the relations that may occur within an intimate public space.
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A (des)ordem doméstica : disposições, desvios e diálogosMonsell, Alice Jean January 2009 (has links)
A pesquisa de Doutorado em Poéticas Visuais, intitulada “A (des)ordem doméstica: Disposições, desvios e diálogos”, do PPGAV/IA/UFRGS, orientada pelo Prof. Dr. Hélio Fervenza desde 2005, partiu da visita a casas de colaboradoras, que registraram a disposição e o display dos objetos de seu lar. Na minha casa, comecei a desenvolver procedimentos táticos de détournement (desvio) das minhas práticas domésticas e artísticas com base em modelos da vida cotidiana – os registros das visitas, os processos domésticos materiais e sociais, sua efemeridade e seus acasos – notando algumas referências na arte: os Tableaux Piéges (Pinturas Armadilhas, 1960-70) de Daniel Spoerri. Gartenskulptur (1968- 96) de Dieter Roth, Gordon Matta-Clark, Kurt Schwitters, bem como a noção de “arte comoa- vida” em Allan Kaprow. Entre 2005 e 2006, emergem procedimentos de desvio (détournement) de processos de uso e da função de objetos domésticos a pa rtir de sua reconstrução, usando como materiais de trabalho as “sobras, que se referem aos objetos inúteis, guardados e acumulados na minha casa. A operação poética, a “to-pó-grafia”, investiga a disposição pelo desvio de um guardanapo de crochê para a função de matrizestêncil coberta com poeira, embaralhando a ordem cultural deste objeto. O gesto doméstico de varrer sofre o desvio através dos “re-enquadramentos”, quando poeira e detritos do chão são transformados em “quadros” pendurados na parede em cima do sofá, problematizando um modelo da arte, bem como um modelo doméstico de disposição e de display. A partir do final de 2006, experimentei com a inserção da documentação fotográfica das visitas em objetos domésticos reais ou reconstruídos. Esse é um dos procedimentos que elabora questões de apresentação pública. Emerge nesta etapa, a proposta de apresentação e display: a domesticação. Essa se refere à operação de “domesticar um espaço não-doméstico”, pela recontextualização. Por exemplo, de uma garagem, uma sala de aula ou galeria, a partir de modelos de disposição observados em casas. A domesticação de uma galeria faz com que a função estética dos objetos e sua função social oscilem, transformando o espaço em meio para fornecer um contexto para diálogo e trocas. Uma das táticas para potencializar tais interações inclui minha presença no espaço de apresentação, em certos dias e horários, para “receber as visitas”, trocar palavras, compartilhar chá com bolachas... visando a instaurar dúvidas sobre a função e a (des)ordem dos objetos ali dispostos e propor outro modelo social para as relações que podem ocorrer dentro de um espaço íntimo público. / The doctoral research project in Visual Poetics, entitled, “Domestic (dis)order: (dis)placements, detours and dialogues”, at the PPGAV/IA/UFRGS, oriented by Professor Hélio Fervenza, PhD since 2005, initially proposed visiting the houses of collaborators who recorded the placement and display of objects in their homes. In my house, I proceeded to develop tactical procedures of détournement (detour) of my domestic and artistic practices based on quotidian models - the records of visits and observed domestic material and social processes, both ephemeral and random - noting some of my references in art: the “Tableaux Piéges” (Snare Pictures) (1960-70) by Daniel Spoerri; “Gartenskulptur” (1968-96) by Dieter Roth; Gordon Matta-Clark, Kurt Schwitters, as well as the notion of “lifelike art” in Allan Kaprow. Between 2005 and 2006, procedures emerge that detour (deturn) the processes of use and the function of domestic objects through their reconstruction, using as work materials the “leftovers”, which refers to all useless objects that had been stored and were accumulating in my home. The “dust-o-graph” investigates the placement of crochet doilies by detouring their everyday function into a graphic tool for stenciling with household dust, shuffling this object’s cultural order. The household gesture of sweeping suffers a detour through the procedure of “re-picturing” when floor dust and scraps are transformed into “pictures” placed hanging on the wall above the sofa, problematizing a model of art, as well as a model of placement and display in the home. Toward the end of 2006, I began to experiment with insertion of photographic documents from visits into real or reconstructed domestic objects. This is one of the procedures developed to elaborate questions involving public presentation. At this stage, the poetic proposal of public presentation and display “domestication” emerges. This refers to the operation of “domesticating a non-domestic space” by recontextualizing, for example, an art gallery, a classroom or a garage using placement models observed in homes. The “domestication” of a gallery makes the aesthetic function of objects and its social order oscillate, transforming the space into a means to offer a context for dialogue and exchanges. One of the tactics for potentializing interactions is my own presence in the presentation space, at certain times, when I “receive visitors”, converse, offer tea and cookies… aiming to place doubt on the function and order of objects (dis)placed there and at proposing an alternative social model for the relations that may occur within an intimate public space.
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A (des)ordem doméstica : disposições, desvios e diálogosMonsell, Alice Jean January 2009 (has links)
A pesquisa de Doutorado em Poéticas Visuais, intitulada “A (des)ordem doméstica: Disposições, desvios e diálogos”, do PPGAV/IA/UFRGS, orientada pelo Prof. Dr. Hélio Fervenza desde 2005, partiu da visita a casas de colaboradoras, que registraram a disposição e o display dos objetos de seu lar. Na minha casa, comecei a desenvolver procedimentos táticos de détournement (desvio) das minhas práticas domésticas e artísticas com base em modelos da vida cotidiana – os registros das visitas, os processos domésticos materiais e sociais, sua efemeridade e seus acasos – notando algumas referências na arte: os Tableaux Piéges (Pinturas Armadilhas, 1960-70) de Daniel Spoerri. Gartenskulptur (1968- 96) de Dieter Roth, Gordon Matta-Clark, Kurt Schwitters, bem como a noção de “arte comoa- vida” em Allan Kaprow. Entre 2005 e 2006, emergem procedimentos de desvio (détournement) de processos de uso e da função de objetos domésticos a pa rtir de sua reconstrução, usando como materiais de trabalho as “sobras, que se referem aos objetos inúteis, guardados e acumulados na minha casa. A operação poética, a “to-pó-grafia”, investiga a disposição pelo desvio de um guardanapo de crochê para a função de matrizestêncil coberta com poeira, embaralhando a ordem cultural deste objeto. O gesto doméstico de varrer sofre o desvio através dos “re-enquadramentos”, quando poeira e detritos do chão são transformados em “quadros” pendurados na parede em cima do sofá, problematizando um modelo da arte, bem como um modelo doméstico de disposição e de display. A partir do final de 2006, experimentei com a inserção da documentação fotográfica das visitas em objetos domésticos reais ou reconstruídos. Esse é um dos procedimentos que elabora questões de apresentação pública. Emerge nesta etapa, a proposta de apresentação e display: a domesticação. Essa se refere à operação de “domesticar um espaço não-doméstico”, pela recontextualização. Por exemplo, de uma garagem, uma sala de aula ou galeria, a partir de modelos de disposição observados em casas. A domesticação de uma galeria faz com que a função estética dos objetos e sua função social oscilem, transformando o espaço em meio para fornecer um contexto para diálogo e trocas. Uma das táticas para potencializar tais interações inclui minha presença no espaço de apresentação, em certos dias e horários, para “receber as visitas”, trocar palavras, compartilhar chá com bolachas... visando a instaurar dúvidas sobre a função e a (des)ordem dos objetos ali dispostos e propor outro modelo social para as relações que podem ocorrer dentro de um espaço íntimo público. / The doctoral research project in Visual Poetics, entitled, “Domestic (dis)order: (dis)placements, detours and dialogues”, at the PPGAV/IA/UFRGS, oriented by Professor Hélio Fervenza, PhD since 2005, initially proposed visiting the houses of collaborators who recorded the placement and display of objects in their homes. In my house, I proceeded to develop tactical procedures of détournement (detour) of my domestic and artistic practices based on quotidian models - the records of visits and observed domestic material and social processes, both ephemeral and random - noting some of my references in art: the “Tableaux Piéges” (Snare Pictures) (1960-70) by Daniel Spoerri; “Gartenskulptur” (1968-96) by Dieter Roth; Gordon Matta-Clark, Kurt Schwitters, as well as the notion of “lifelike art” in Allan Kaprow. Between 2005 and 2006, procedures emerge that detour (deturn) the processes of use and the function of domestic objects through their reconstruction, using as work materials the “leftovers”, which refers to all useless objects that had been stored and were accumulating in my home. The “dust-o-graph” investigates the placement of crochet doilies by detouring their everyday function into a graphic tool for stenciling with household dust, shuffling this object’s cultural order. The household gesture of sweeping suffers a detour through the procedure of “re-picturing” when floor dust and scraps are transformed into “pictures” placed hanging on the wall above the sofa, problematizing a model of art, as well as a model of placement and display in the home. Toward the end of 2006, I began to experiment with insertion of photographic documents from visits into real or reconstructed domestic objects. This is one of the procedures developed to elaborate questions involving public presentation. At this stage, the poetic proposal of public presentation and display “domestication” emerges. This refers to the operation of “domesticating a non-domestic space” by recontextualizing, for example, an art gallery, a classroom or a garage using placement models observed in homes. The “domestication” of a gallery makes the aesthetic function of objects and its social order oscillate, transforming the space into a means to offer a context for dialogue and exchanges. One of the tactics for potentializing interactions is my own presence in the presentation space, at certain times, when I “receive visitors”, converse, offer tea and cookies… aiming to place doubt on the function and order of objects (dis)placed there and at proposing an alternative social model for the relations that may occur within an intimate public space.
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Exploring Alternative Routes Using Multipath TCPBrennan, Stephen 30 August 2017 (has links)
No description available.
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內與外的迂迴: 簡愛的詩意與政治 / Detouring: the Poetics and Politics of Jane Eyre劉依綺, Liu, Yi-chi Unknown Date (has links)
《簡愛》如同吳爾芙所說的「強烈的自我中心性格」、借力於詩意的雄渾寫景、狹窄的力度,這些特質標誌著《簡愛》或夏綠蒂勃朗蒂獨樹一幟的文體風格。此外據吳爾芙的剖析,十九世紀英國女作家所寫小說必然受到狹窄的生活經驗所影響,作者性格總通過某種個人的因素而被清楚的意識。本文一方面通過現象學式的稠密閱╱寫對《簡愛》這部小說的上述特質加以印證、詮釋;同時也在性別政治脈絡的還原過程中將寫作活動的理論引曵回歷史情境,為文化情境中所謂「局部壓抑」的迷思做預先的鋪陳。在方法上,本文首先根據《簡愛》的「空間」與「物」的呈現╱陳列特質,演繹出該作品內建「狹窄的自我中心性」,這個中心是以童年的場景作為整部小說的詩意原型,同時整部小說也以摧毀童年夢靨原型為逆轉點。在詳細的分析後我們將發現,勃朗蒂竟是十分勉強地安排性別政治的標準價值,愛情與婚姻的價值、情感的脆弱、家庭事物的價值…這一切在《簡愛》這部小說裡,在通過帶著現象學傾向的分析後,我們將一一發現作者曾試圖想消除、重寫那些標準價值的痕跡,同時也發現那些不穩定的、不一致的事件串連事實上是通過「視覺物」被讀者的預設所任意完整化的。一當經過仔細的分析後我們發現這部故事並未以因果的方式開展出結果,反而我們發現一個又一個的空間為不存在的主體進行補充試圖刻畫出一個新的女性標準。綜觀《簡愛》整部作品可演繹出以下敘事模式與原則:fiction(構作)—simulation(擬仿)—supplement/ reverse (補充/逆轉)。本文認為這個敘事原則在過去採取精神分析假設與後殖民論述立場的分析裡被嚴重忽略,甚至扭曲女性書寫活動裡的情緒張力成為帝國慾望的再現;本文以顛倒順
序的閱讀方式重行分析出上述勃朗蒂的敘事模式,也提出非線共時平
面觀點的閱╱寫分析。 / Virginia Woolf points out that the circumstances which affected an author’s character may have left their traces on their work; therefore, the writings of nineteenth-century female writers are arguably affected by their limited life experience. In an effort to analyse the self-enclosure in Jane Eyre, this thesis first examines the theme of narrowness by employing a method of phenomenological thick reading/writing. I will argue that Jane Eyre constructs Jane’s childhood as a poetic prototype and centres on the end of Jane’s childhood nightmare as a turning point. Moreover, after close analysis of the text, it will be found that Brontë manages to arrange the standard of sexual politics, the value of family, love, and marriage with difficulty. By applying a phenomenological reading, we will find traces that the author tries to erase or rewrite these values. The reading of materiality, silence, space, and conflict within texts will open up extremely productive ways of studying the politics of language. The inconsistency, rupture, and disjunction of incidents are freely associated as a unity, a consistent novel by readers through the appearance of objects, and the plot of Jane Eyre is not based upon cause-and-effect. The narrative mode of Jane Eyre can be interpreted as fiction-simulation-supplement/reverse. The centrality of this narrative technique to Brontë’s work has received little attention in psychoanalytic or postcolonial criticism, both of which often interpret the intensity of feeling of the novel as the embodiment of imperial desire. By employing a non-linear reading of Jane Eyre, I will examine the narrative in reverse order, trying to establish a new platform for the infinite interplay between author, reader, and characters.
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La conjecture de partitionnement des cheminsChampagne-Paradis, Audrey 05 1900 (has links)
Soit G = (V, E) un graphe simple fini. Soit (a, b) un couple d’entiers positifs. On note par τ(G) le nombre de sommets d’un chemin d’ordre maximum dans G. Une partition (A,B) de V(G) est une (a,b)−partition si τ(⟨A⟩) ≤ a et τ(⟨B⟩) ≤ b. Si G possède une (a, b)−partition pour tout couple d’entiers positifs satisfaisant τ(G) = a+b, on dit que G est τ−partitionnable. La conjecture de partitionnement des chemins, connue sous le nom anglais de Path Partition Conjecture, cherche à établir que tout graphe est τ−partitionnable. Elle a été énoncée par Lovász et Mihók en 1981 et depuis, de nombreux chercheurs ont tenté de démontrer cette conjecture et plusieurs y sont parvenus pour certaines classes de graphes. Le présent mémoire rend compte du statut de la conjecture, en ce qui concerne les graphes non-orientés et ceux orientés. / Let G = (V,E) be a finite simple graph. We denote the number of vertices in a longest path in G by τ(G). A partition (A,B) of V is called an (a,b)−partition if τ(⟨A⟩) ≤ a and τ(⟨B⟩) ≤ b. If G can be (a,b)−partitioned for every pair of positive integers (a, b) satisfying a + b = τ (G), we say that G is τ −partitionable. The following conjecture, called The Path Partition Conjecture, has been stated by Lovász and Mihók in 1981 : every graph is τ−partitionable. Since that, many researchers prove that this conjecture is true for several classes of graphs and digraphs. This study summarizes the different results about the Path Partition conjecture.
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