Concept
Graphe cordal
Concepts associés (47)
Graphe chenille
thumb|upright=1.2|Un graphe chenille. En théorie des graphes, un graphe chenille ou plus simplement une chenille est un arbre dans lequel tous les sommets sont à distance au plus 1 d'un chemin central. Les graphes chenilles ont d'abord été étudiés dans une série d'articles de Harary et Schwenk. Le nom a été suggéré par A. Hobbs. Harary & Schwenk écrivent de façon colorée : « une chenille est un arbre qui se métamorphose en un chemin lorsque son cocon de points d'extrémité est supprimé ».
Complexité paramétrée
En algorithmique, la complexité paramétrée (ou complexité paramétrique) est une branche de la théorie de la complexité qui classifie les problèmes algorithmiques selon leur difficulté intrinsèque en fonction de plusieurs paramètres sur les données en entrée ou sur la sortie. Ce domaine est étudié depuis les années 90 comme approche pour la résolution exacte de problèmes NP-complets. Cette approche est utilisée en optimisation combinatoire, notamment en algorithmique des graphes, en intelligence artificielle, en théorie des bases de données et en bio-informatique.
Grundy number
In graph theory, the Grundy number or Grundy chromatic number of an undirected graph is the maximum number of colors that can be used by a greedy coloring strategy that considers the vertices of the graph in sequence and assigns each vertex its first available color, using a vertex ordering chosen to use as many colors as possible. Grundy numbers are named after P. M. Grundy, who studied an analogous concept for directed graphs in 1939. The undirected version was introduced by .
Clique graph
In graph theory, a clique graph of an undirected graph G is another graph K(G) that represents the structure of cliques in G. Clique graphs were discussed at least as early as 1968, and a characterization of clique graphs was given in 1971. A clique of a graph G is a set X of vertices of G with the property that every pair of distinct vertices in X are adjacent in G. A maximal clique of a graph G is a clique X of vertices of G, such that there is no clique Y of vertices of G that contains all of X and at least one other vertex.
Circle graph
In graph theory, a circle graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with a finite system of chords of a circle such that two vertices are adjacent if and only if the corresponding chords cross each other. gives an O(n2)-time algorithm that tests whether a given n-vertex undirected graph is a circle graph and, if it is, constructs a set of chords that represents it. A number of other problems that are NP-complete on general graphs have polynomial time algorithms when restricted to circle graphs.
Chordal bipartite graph
In the mathematical area of graph theory, a chordal bipartite graph is a bipartite graph B = (X,Y,E) in which every cycle of length at least 6 in B has a chord, i.e., an edge that connects two vertices that are a distance > 1 apart from each other in the cycle. A better name would be weakly chordal and bipartite since chordal bipartite graphs are in general not chordal as the induced cycle of length 4 shows. Chordal bipartite graphs have various characterizations in terms of perfect elimination orderings, hypergraphs and matrices.
Chordal completion
In graph theory, a branch of mathematics, a chordal completion of a given undirected graph G is a chordal graph, on the same vertex set, that has G as a subgraph. A minimal chordal completion is a chordal completion such that any graph formed by removing an edge would no longer be a chordal completion. A minimum chordal completion is a chordal completion with as few edges as possible. A different type of chordal completion, one that minimizes the size of the maximum clique in the resulting chordal graph, can be used to define the treewidth of G.