Generalized clique family inequalities for claw-free graphs
نویسندگان
چکیده
منابع مشابه
Clique family inequalities for the stable set polytope of quasi-line graphs
In one of fundamental work in combinatorial optimization Edmonds gave a complete linear description of the matching polytope. Matchings in a graph are equivalent to stable sets its line graph. Also the neighborhood of any vertex in a line graph partitions into two cliques: graphs with this latter property are called quasi-line graphs. Quasi-line graphs are a subclass of claw-free graphs, and as...
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In this thesis we focus our attention on the stable set polytope of claw-free graphs. This problem has been open for many years and albeit all the efforts engaged during those last three years, it is still open. This does not mean that no progress has been made and we hope to the contrary that this thesis contains some important advances and that the reader will share this point of view. Unders...
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It is a long standing open problem to find an explicit description of the stable set polytope of claw-free graphs. Yet more than 20 years after the discovery of a polynomial algorithm for the maximum stable set problem for claw-free graphs, there is even no conjecture at hand today. Such a conjecture exists for the class of quasi-line graphs. This class of graphs is a proper superclass of line ...
متن کاملClique minors in claw-free graphs
Hadwiger’s conjecture states that every graph with chromatic number χ has a clique minor of size χ. Let G be a graph on n vertices with chromatic number χ and stability number α. Then since χα ≥ n, Hadwiger’s conjecture implies that G has a clique minor of size n α . In this paper we prove that this is true for connected claw-free graphs with α ≥ 3. We also show that this result is tight by pro...
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It is a long standing open problem to find an explicit description of the stable set polytope of clawfree graphs. Yet more than 20 years after the discovery of a polynomial algorithm for the maximum stable set problem for claw-free graphs, there is even no conjecture at hand today. Such a conjecture exists for the class of quasi-line graphs. This class of graphs is a proper superclass of line g...
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ورودعنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 25 شماره
صفحات -
تاریخ انتشار 2006