77544
20180317093159.0
7279
DAR
000230361400022
ISI
REP_WORK
Circular Ones Matrices and the Stable Set Polytope of Quasi-Line Graphs
2004
2004
Reports
RO 2004.1116
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. 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.
Eisenbrand, F.
183121
240331
Oriolo, G.
Stauffer, G.
149637
240346
Ventura, P.
oai:infoscience.tind.io:77544
report
SB
DISOPT
252111
U11879
ROSO
252055
ROSO-REPORT-2004-002
Eisenbrand2004_811/ROSO
EPFL
PUBLISHED
REPORT