Weighted graphs defining facets: A connection between stable set and linear ordering polytopes
نویسندگان
چکیده
منابع مشابه
Weighted graphs defining facets: A connection between stable set and linear ordering polytopes
A graph is α-critical if its stability number increases whenever an edge is removed from its edge set. The class of α-critical graphs has several nice structural properties, most of them related to their defect which is the number of vertices minus two times the stability number. In particular, a remarkable result of Lovász (1978) is the finite basis theorem for α-critical graphs of a fixed def...
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Providing a complete description of the stable set polytopes of claw-free graphs is a longstanding open problem since almost twenty years. Eisenbrandt et al. recently achieved a breakthrough for the subclass of quasi-line graphs. As a consequence, every non-trivial facet of their stable set polytope is of the form k ∑ v∈V1 xv+(k+1) ∑ v∈V2 xv ≤ b for some positive integers k and b, and non-empty...
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The binary choice polytope appeared in the investigation of the binary choice problem formulated by Guilbaud (1953) and Block and Marschak (1960). It is nowadays known to be the same as the linear ordering polytope from operations research (Grötschel, Jünger and Reinelt, 1985). The central problem is to find facet-defining linear inequalities for the polytope. Fence inequalities constitute a pr...
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Grotschel, Lovhz and Schrijver introduced a convex set containing the stable set polytope of a graph. They proved that the set is a polytope if and only if the corresponding graph is perfect. In this paper, we give an alternative proof of the fact based on a new representation of the convex set described by infinitely many convex quadratic inequalities.
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ژورنال
عنوان ژورنال: Discrete Optimization
سال: 2009
ISSN: 1572-5286
DOI: 10.1016/j.disopt.2008.07.001