The stable set polytope of quasi-line graphs

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 graphs and a proper subclass of claw-free graphs for which it is known that not all facets have 0/1 normal vectors. The Ben Rebea conjecture states that the stable set polytope of a quasi-line graph is completely described by clique-family inequalities. Chudnovsky and Seymour recently provided a decomposition result for claw-free graphs and proved that the Ben Rebea conjecture holds, if the quasi-line graph is not a fuzzy circular interval graph. In this paper, we give a proof of the Ben Rebea conjecture by showing that it also holds for fuzzy circular interval graphs. Our result builds upon an a...

• Type: Journal
• Year: 2008
• Where: COMBINATORICA
• Authors: Friedrich Eisenbrand, Gianpaolo Oriolo, Gautier Stauffer, Paolo Ventura
• Keywords: Ben Rebea Conjecture, Claw-free Graphs, COMBINATORICA 2008, Stable Set Polytope