000077544 001__ 77544 000077544 005__ 20180317093159.0 000077544 02470 $$2DAR$$a7279 000077544 02470 $$2ISI$$a000230361400022 000077544 037__ $$aREP_WORK 000077544 245__ $$aCircular Ones Matrices and the Stable Set Polytope of Quasi-Line Graphs 000077544 269__ $$a2004 000077544 260__ $$c2004 000077544 336__ $$aReports 000077544 500__ $$aRO 2004.1116 000077544 520__ $$aIt is a long standing open problem to find an explicit description of the stable set polytope of claw-free graphs. Yet more than 20 years after the discovery of a polynomial algorithm for the maximum stable set problem for claw-free graphs, there is even no conjecture at hand today. Such a conjecture exists for the class of quasi-line graphs. This class of graphs is a proper superclass of line graphs and a proper subclass of claw-free graphs for which it is known that not all facets have 0/1 normal vectors. Ben Rebea's conjecture states that the stable set polytope of a quasi-line graph is completely described by clique-family inequalities. Chudnovsky and Seymour recently provided a decomposition result for claw-free graphs and proved that Ben Rebea's conjecture holds, if the quasi-line graph is not a fuzzy circular interval graph. In this paper, we give a proof of Ben Rebea's conjecture by showing that it also holds for fuzzy circular interval graphs. Our result builds upon an algorithm of Bartholdi, Orlin and Ratliff which is concerned with integer programs defined by circular ones matrices. 000077544 700__ $$0240331$$aEisenbrand, F.$$g183121 000077544 700__ $$aOriolo, G. 000077544 700__ $$0240346$$aStauffer, G.$$g149637 000077544 700__ $$aVentura, P. 000077544 909CO $$ooai:infoscience.tind.io:77544$$pSB$$preport 000077544 909C0 $$0252111$$pDISOPT$$xU11879 000077544 909C0 $$0252055$$pROSO 000077544 937__ $$aROSO-REPORT-2004-002 000077544 970__ $$aEisenbrand2004_811/ROSO 000077544 973__ $$aEPFL$$sPUBLISHED 000077544 980__ $$aREPORT