Even-hole-free graphs part II: Recognition algorithm
نویسندگان
چکیده
منابع مشابه
Even-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.
متن کاملEven-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 کاملA faster algorithm to recognize even-hole-free graphs
Article history: Received 10 August 2013 Available online 11 February 2015
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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, ...
متن کاملBisimplicial vertices in even-hole-free graphs
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...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2002
ISSN: 0364-9024
DOI: 10.1002/jgt.10045