Literatura científica selecionada sobre o tema "Contraction perfect graphs"

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Artigos de revistas sobre o assunto "Contraction perfect graphs"

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Diner, Öznur Yaşar, Daniël Paulusma, Christophe Picouleau e Bernard Ries. "Contraction and deletion blockers for perfect graphs and H-free graphs". Theoretical Computer Science 746 (outubro de 2018): 49–72. http://dx.doi.org/10.1016/j.tcs.2018.06.023.

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Bertschi, Marc E. "Perfectly contractile graphs". Journal of Combinatorial Theory, Series B 50, n.º 2 (dezembro de 1990): 222–30. http://dx.doi.org/10.1016/0095-8956(90)90077-d.

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Maffray, Frédéric, e Nicolas Trotignon. "Algorithms for Perfectly Contractile Graphs". SIAM Journal on Discrete Mathematics 19, n.º 3 (janeiro de 2005): 553–74. http://dx.doi.org/10.1137/s0895480104442522.

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Sales, Cláudia Linhares, Frédéric Maffray e Bruce Reed. "On Planar Perfectly Contractile Graphs". Graphs and Combinatorics 13, n.º 2 (junho de 1997): 167–87. http://dx.doi.org/10.1007/bf03352994.

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Rusu, Irena. "Perfectly contractile diamond-free graphs". Journal of Graph Theory 32, n.º 4 (dezembro de 1999): 359–89. http://dx.doi.org/10.1002/(sici)1097-0118(199912)32:4<359::aid-jgt5>3.0.co;2-u.

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Sales, Cláudia Linhares, e Frédéric Maffray. "On dart-free perfectly contractile graphs". Theoretical Computer Science 321, n.º 2-3 (agosto de 2004): 171–94. http://dx.doi.org/10.1016/j.tcs.2003.11.026.

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Lévêque, Benjamin, e Frédéric Maffray. "Coloring Bull-Free Perfectly Contractile Graphs". SIAM Journal on Discrete Mathematics 21, n.º 4 (janeiro de 2008): 999–1018. http://dx.doi.org/10.1137/06065948x.

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Maffray, Frédéric, e Nicolas Trotignon. "A class of perfectly contractile graphs". Journal of Combinatorial Theory, Series B 96, n.º 1 (janeiro de 2006): 1–19. http://dx.doi.org/10.1016/j.jctb.2005.06.011.

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PANDA, SWARUP. "Inverses of bicyclic graphs". Electronic Journal of Linear Algebra 32 (6 de fevereiro de 2017): 217–31. http://dx.doi.org/10.13001/1081-3810.3322.

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A graph G is said to be nonsingular (resp., singular) if its adjacency matrix A(G) is nonsingular (resp., singular). The inverse of a nonsingular graph G is the unique weighted graph whose adjacency matrix is similar to the inverse of the adjacency matrix A(G) via a diagonal matrix of ±1s. Consider connected bipartite graphs with unique perfect matchings such that the graph obtained by contracting all matching edges is also bipartite. In [C.D. Godsil. Inverses of trees. Combinatorica, 5(1):33–39, 1985.], Godsil proved that such graphs are invertible. He posed the question of characterizing the bipartite graphs with unique perfect matchings possessing inverses. In this article, Godsil’s question for the class of bicyclic graphs is answered.
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Fischer, Ilse, e C. H. C. Little. "Even Circuits of Prescribed Clockwise Parity". Electronic Journal of Combinatorics 10, n.º 1 (24 de novembro de 2003). http://dx.doi.org/10.37236/1738.

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We show that a graph has an orientation under which every circuit of even length is clockwise odd if and only if the graph contains no subgraph which is, after the contraction of at most one circuit of odd length, an even subdivision of $K_{2,3}$. In fact we give a more general characterisation of graphs that have an orientation under which every even circuit has a prescribed clockwise parity. Moreover we show that this characterisation has an equivalent analogue for signed graphs. We were motivated to study the original problem by our work on Pfaffian graphs, which are the graphs that have an orientation under which every alternating circuit is clockwise odd. Their significance is that they are precisely the graphs to which Kasteleyn's powerful method for enumerating perfect matchings may be applied.
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Teses / dissertações sobre o assunto "Contraction perfect graphs"

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Dupont, Bouillard Alexandre. "Co-k-plexes and k-defective coloring : polytopes and algorithms". Electronic Thesis or Diss., Paris 13, 2024. http://www.theses.fr/2024PA131019.

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Cette thèse propose plusieurs résultats sur les co-k-plexes, qui sont des ensembles de sommets induisant un graphe avec un degré maximum k-1. La première partie de la thèse explore plusieurs caractérisations d'une nouvelle sous-classe de graphes parfaits, appelés graphes contraction parfaits. Ce sont l'ensemble des graphes parfaits restant parfaits après contraction de n'importe quel ensemble d'arêtes. Cette classe de graphes est caractérisée de quatre manières différentes. Parmi ces résultats, un graphe est contraction parfait si et seulement s'il est parfait et que la contraction de n'importe quelle arête préserve sa perfection. Cela permet une caractérisation des graphes contraction parfait en termes de sous-graphes induits interdits, ainsi qu'un algorithme polynomial pour leur reconnaissance. Le utter graphe u(G) d'un graphe G est un graphe dont les stables sont en bijection avec les co-2-plexes de G. Il est démontré que u(G) est parfait si et seulement si G est contraction parfait. Puisque le problème de stable de poids maximum est solvable en temps polynomial sur les graphes parfaits, il en va de même pour le problème de co-2-plex de poids max sur les graphes contraction parfait. Une formulation étendue pour le polytope co-2-plex des graphes contraction parfait est obtenue en considérant le polytope de l'ensemble des stable de son utter graphe. Notez que cette formulation devient compacte pour les graphes chordaux. De plus, avec des contraintes d'intégrité, cette formulation devient une formulation ILP valide pour n'importe quel graphe G, conduisant à une comparaison entre cette formulation ILP étendue et la formulation classique de la littérature. D'un point de vue théorique, cette nouvelle formulation a une relaxation linéaire de meilleure qualité, et d'un point de vue expérimental, plusieurs implémentations de cette nouvelle formulation sont proposées et se révèlent compétitives. La deuxième partie de la thèse concerne le problème k-defective coloring qui consiste à recouvrir les sommets d'un graphe avec un nombre minimum de co-k-plexes. Ce problème est formulé comme une formulation set covering contenant une variable par co-k-plex, et résolu en utilisant une méthode de branch and price. Un algorithme de branch and price pour le k-defective coloring proposé par Furini et al. est d'abord décrit et mis en œuvre en utilisant le framework SCIP, et plusieurs améliorations sont proposées pour les cas k=1,2. Cette thèse propose plusieurs alternances entre les phases de cutting et de pricing et en particulier deux stratégies paramétrées sont conçues pour se débarrasser du tailing off effect. La génération de colonnes peut aussi être stabilisée en utilisant des inégalités optimales duales. Cette technique consiste à ajouter au RMP un ensemble de colonnes supplémentaires correspondant à des inégalités ne coupant aucun point optimal du problème dual. Cette méthode est expérimentalement efficace pour stabiliser la génération de colonnes à chaque nœud de l'arbre de branchement. Différentes façons de combiner les inégalités de renforcement et les inégalités optimales duales sont étudiées. Pour k=2, le problème de pricing se réduit à calculer un problème de co-2-plex pondéré maximum. Par conséquent, une variante de la méthode de branch and price dans laquelle le pricing est résolu en utilisant la formulation ILP de la première partie de la thèse est évaluée expérimentalement. De nouvelles inégalités duales sont proposées pour la stabilisation du cas k=2. Contrairement à ce qui existe dans la littérature, les inégalités duales proposées peuvent couper chaque solution optimale du dual. Cependant, chaque solution primale entière avec des valeurs positives dans les colonnes supplémentaires peut être transformée en une solution entière du problème d'origine avec la même valeur optimale. Une amélioration expérimentale significative est observée pour le problème de 2-defective coloring
This thesis proposes several results about co-k-plexes, which are vertex sets inducing a graph with maximum degree k-1 and the k-defective coloring which consists in covering the vertices of a graph with a minimum number of co-k-plexes. The thesis is split into two parts, each starting with a dedicated state-of-the-art chapter.The first part investigates several characterizations of a new subclass of perfect graphs that we call contraction-perfect graphs, which is the set of perfect graphs remaining perfect after the contraction of any edge set.Contractions in perfect graphs: We characterize this graph class in four different manners.We give a characterization of contraction-perfect graphs in terms of forbidden induced subgraphs, and a polynomial algorithm to recognize them. On such graphs, solving the maximum weighted co-2-plex problem is doable in polynomial time. This is done by considering what we call the utter graph u(G) of a graph G, whose stable sets are in bijection with the co-2-plexes of G. We show that u(G) is perfect if and only if G is contraction-perfect and as the maximum stable set problem is solvable in polynomial time on perfect graphs we obtain the polynomiality result of the maximum weighted co-2-plex problem on contraction-perfect graphs.The maximum weighted co-2-plex problem : We investigate an extended formulation for the co-2-plex polytope of contraction-perfect graphs obtained by considering the stable set polytope of its utter graph. Note that this formulation becomes compact for chordal graphs. Moreover, with additional integrity constraints, this formulation becomes a valid ILP formulation for any graph G, leading to a comparison between this extended ILP formulation with a formulation of the literature. From an experimental point of view, we propose different implementation variants of our formulation and conclude that they are competitive with the one from the literature. The second part of the thesis is about column generation: we describe a method from the literature solving the k-defective coloring proposed by Furini et al. We then implement this method within the SCIP framework to let us add new techniques.The graph coloring problem and alternation strategies: Column generation is known to suffer from the tailing off effect that consists of a sequence of non-improving subsets of variables. To tackle this issue, we tried to alternate between cutting and pricing and in particular proposed two parameterized strategies hoping that cutting earlier would help to get rid of the tailing-off effect. The second improvement of this framework has been proposed in the literature under the name of {dual optimal inequalities}: this technique consists in adding to the RMP a set of columns that are inequalities cutting no optimal points of the dual RMP. This method has been experimentally successful in stabilizing the column generation for the case k=1, we hence tried to combine primal/dual inequalities and alternation strategies in several manners. For the case k=2 we propose to use dedicated valid inequalities, called triangle constraints. We also propose a set of dual inequalities for any k and showed that it implied significant improvements. We then applied a technique similar to our work on the case k=1 combining primal and dual inequalities, for the case k=2. Note that the dual inequalities we propose are of a new type that has not been investigated in the literature: they may cut every dual optimal point but, when considered as variables of the primal, they never add integer solutions that cannot be mapped into an integer solution of the original problem with the same optimum value. Finally, we recap the results of the thesis and give perspectives for each of the chapters
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Capítulos de livros sobre o assunto "Contraction perfect graphs"

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Linhares Sales, Cláudia, e Frédéric Maffray. "On Dart-Free Perfectly Contractile Graphs Extended Abstract". In Lecture Notes in Computer Science, 135–44. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/10719839_15.

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