@misc{PecherWagler2003, author = {P{\^e}cher, Arnaud and Wagler, Annegret}, title = {A construction for non-rank facets of stable set polytopes of webs}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7437}, number = {03-21}, year = {2003}, abstract = {Graphs with circular symmetry, called webs, are relevant for describing the stable set polytopes of two larger graph classes, quasi-line graphs [{\sl Giles and Trotter 1981, Oriolo 2001}] and claw-free graphs [{\sl Galluccio and Sassano 1997, Giles and Trotter 1981}]. Providing a decent linear description of the stable set polytopes of claw-free graphs is a long-standing problem [{\sl Gr{\"o}tschel, Lov\'asz, and Schrijver 1988}]. However, even the problem of finding all facets of stable set polytopes of webs is open. So far, it is only known that stable set polytopes of webs with clique number \$\leq 3\$ have rank facets only [{\sl Dahl 1999, Trotter 1975}] while there are examples with clique number \$\geq 4\$ having non-rank facets [{\sl e.g. Liebling et al. 2003, Oriolo 2001, P\^echer and Wagler 2003}]. In this paper, we provide a construction for non-rank facets of stable set polytopes of webs. We use this construction to prove, for several fixed values of \$\omega\$ including all odd values at least 5, that there are only finitely many webs with clique number \$\omega\$ whose stable set polytopes admit rank facets only.}, language = {en} }