Sciweavers

ENDM
2007

On facets of stable set polytopes of claw-free graphs with stability number three

13 years 11 months ago
On facets of stable set polytopes of claw-free graphs with stability number three
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 sets of vertices V1 and V2. Roughly speaking, this states that the facets of the stable set polytope of quasi-line graphs have at most two left coefficients. For stable set polytopes of claw-free graphs with maximum stable set size at least four, Stauffer conjectured in 2005 that this still holds. It is already known that some stable set polytopes of claw-free graphs with maximum stable set size three may have facets with up to 5 left coefficients. We prove that the situation is even worse: for every positive integer b, there is a clawfree graph with stability number three whose stable set...
Arnaud Pêcher, Pierre Pesneau, Annegret Wagl
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2007
Where ENDM
Authors Arnaud Pêcher, Pierre Pesneau, Annegret Wagler
Comments (0)