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Chordal graphs are precisely the graphs that are both odd-hole-free and even-hole-free (see holes in graph theory). Every chordal graph is a strangulated graph , a graph in which every peripheral cycle is a triangle, because peripheral cycles are a special case of induced cycles.
In the mathematical area of graph theory, an undirected graph G is strongly chordal if it is a chordal graph and every cycle of even length (≥ 6) in G has an odd chord, i.e., an edge that connects two vertices that are an odd distance (>1) apart from each other in the cycle. [1]
A perfect graph is a graph in which, for every induced subgraph, the size of the maximum clique equals the minimum number of colors in a coloring of the graph; perfect graphs include many well-known graph classes including the bipartite graphs, chordal graphs, and comparability graphs.
In graph theory, the perfect graph theorem of László Lovász (1972a, 1972b) states that an undirected graph is perfect if and only if its complement graph is also perfect. This result had been conjectured by Berge ( 1961 , 1963 ), and it is sometimes called the weak perfect graph theorem to distinguish it from the strong perfect graph theorem ...
Cycle graph, a graph that consists of a single cycle; Chordal graph, a graph in which every induced cycle is a triangle; Directed acyclic graph, a directed graph with no directed cycles; Forest, a cycle-free graph; Line perfect graph, a graph in which every odd cycle is a triangle; Perfect graph, a graph with no induced cycles or their ...
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. Chordal completions can also be used to characterize several other graph classes including AT-free ...
The graph of the 3-3 duoprism (the line graph of ,) is perfect.Here it is colored with three colors, with one of its 3-vertex maximum cliques highlighted. In graph theory, a perfect graph is a graph in which the chromatic number equals the size of the maximum clique, both in the graph itself and in every induced subgraph.
Graph minor Diestel (2000), [1] p. 275: Apex graphs: A finite obstruction set Graph minor [3] Linklessly embeddable graphs: The Petersen family: Graph minor [4] Bipartite graphs: Odd cycles Subgraph [5] Chordal graphs: Cycles of length 4 or more Induced subgraph [6] Perfect graphs: Cycles of odd length 5 or more or their complements: Induced ...