No odd pairs in minimal imperfect NP5 graphs
β Scribed by Jean-Luc Fouquet
- Book ID
- 104136739
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 55 KB
- Volume
- 83
- Category
- Article
- ISSN
- 0020-0190
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π SIMILAR VOLUMES
proved that no minimal imperfect graph has a small transversal, that is, a set of vertices of cardinality at most x + M-1 which meets every c+clique and every x-stable set. In this paper we prove that a slight generalization of this notion of small transversal leads to a conjecture which is as stro
An edge of a graph is called critical, if deleting it the stability number of the graph increases, and a nonedge is called co-critical, if adding it to the graph the size of the maximum clique increases. We prove in this paper, that the minimal imperfect graphs containing certain configurations of t
V. Chva tal conjectured in 1985 that a minimal imperfect graph G cannot have a skew cutset (i.e., a cutset S decomposable into disjoint sets A and B joined by all possible edges). We prove here the conjecture in the particular case where at least one of A and B is a stable set. 2001 Elsevier Science
We show that a minimal imperfect graph \(G\) cannot contain a cutset \(C\) which induces a complete multi-partite graph unless \(C\) is a stable set and \(G\) is an odd hole. This generalizes a result of Tucker, who proved that the only minimal imperfect graphs containing stable cutsets are the odd