On 4-connected claw-free well-covered graphs
نویسندگان
چکیده
منابع مشابه
Well-Covered Claw-Free Graphs
We prove the existence of a polynomial time algorithm to tell whether a graph, with no induced subgraph isomorphic to K1.3 , is well covered. A graph is wellcovered if all its maximal independent sets are of the same cardinality. The problem is known to be polynomialy solvable where the input graph is a line graph and it is NP-hard for the larger family of all graphs which do not contain an ind...
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A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For every graph G, the set of weight functions w such that G is w-well-covered is a vector space. Given an input claw-free graph G, we present an O (
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We consider the existence of several different kinds of factors in 4-connected claw-free graphs. This is motivated by the following two conjectures which are in fact equivalent by a recent result of the third author. Conjecture 1 (Thomassen): Every 4-connected line graph is hamiltonian, i.e. has a connected 2-factor. Conjecture 2 (Matthews and Sumner): Every 4-connected claw-free graph is hamil...
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A graph G is said to be pancyclic if G contains cycles of all lengths from 3 to |V (G)|. We show that if G is 4-connected, claw-free, and P10-free, then G is either pancyclic or it is the line graph of the Petersen graph. This implies that every 4-connected, claw-free, P9-free graph is pancyclic, which is best possible and extends a result of Gould et al. Pancyclicity in 3-connected graphs: Pai...
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A graph G is quadrangularly connected if for every pair of edges e1 and e2 in E(G), G has a sequence of l-cycles (3 ≤ l ≤ 4) C1, C2, ..., Cr such that e1 ∈ E(C1) and e2 ∈ E(Cr) and E(Ci) ∩ E(Ci+1) 6= ∅ for i = 1, 2, ..., r − 1. In this paper, we show that every quadrangularly connected claw-free graph without vertices of degree 1, which does not contain an induced subgraph H isomorphic to eithe...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1996
ISSN: 0166-218X
DOI: 10.1016/0166-218x(94)00117-v