On the Stable Set Polytope of Claw-Free Graphs
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Gear Composition of Stable Set Polytopes and G-Perfection
Mathematics of Operations Research
Note: Facet-inducing web and antiweb inequalities for the graph coloring polytope
Discrete Applied Mathematics
Domination when the stars are out
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Coloring fuzzy circular interval graphs
European Journal of Combinatorics
Gear composition and the stable set polytope
Operations Research Letters
Operations Research Letters
On the facets of the stable set polytope of quasi-line graphs
Operations Research Letters
Stable sets, corner polyhedra and the Chvátal closure
Operations Research Letters
On optimal k-fold colorings of webs and antiwebs
Discrete Applied Mathematics
Minimum weighted clique cover on strip-composed perfect graphs
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Hi-index | 0.00 |
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 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 algorithm of Bartholdi, Orlin and Ratliff which is concerned with integer programs defined by circular ones matrices.