Even-hole-free graphs part I: Decomposition theorem
نویسندگان
چکیده
منابع مشابه
Even-hole-free graphs part I: Decomposition theorem
We prove a decomposition theorem for even-hole-free graphs. The decompositions used are 2-joins and star, double-star and triple-star cutsets. This theorem is used in the second part of this paper to obtain a polytime recognition algorithm for even-hole-free graphs.
متن کاملEven-hole-free graphs part II: Recognition algorithm
We present an algorithm that determines in polytime whether a graph contains an even hole. The algorithm is based on a decomposition theorem for even-hole-free graphs obtained in Part I of this paper. We also give a polytime algorithm to nd an even hole in a graph when one exists.
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An even-hole-free graph is a graph that does not contain, as an induced subgraph, a chordless cycle of even length. A graph is triangulated if it does not contain any chordless cycle of length greater than three, as an induced subgraph. We prove that every even-hole-free graph has a node whose neighborhood is triangulated. This implies that in an even-hole-free graph, with n nodes and m edges, ...
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A hole in a graph is an induced subgraph which is a cycle of length at least four. A hole is called even if it has an even number of vertices. An even-hole-free graph is a graph with no even holes. A vertex of a graph is bisimplicial if the set of its neighbours is the union of two cliques. In this paper we prove that every even-hole-free graph has a bisimplicial vertex, which was originally co...
متن کاملEven-hole-free graphs: a survey
The class of even-hole-free graphs is structurally quite similar to the class of perfect graphs, which was the key initial motivation for their study. The techniques developed in the study of even-hole-free graphs were generalized to other complex hereditary graph classes, and in the case of perfect graphs led to the famous resolution of the Strong Perfect Graph Conjecture and their polynomial ...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2001
ISSN: 0364-9024
DOI: 10.1002/jgt.10006