On Non-Rank Facets of Stable Set Polytopes of Webs with Clique Number Four-Extended Abstract-

Graphs with circular symmetry, called webs, are relevant for describing the stable set polytopes of two larger graph classes, quasi-line graphs [6,10] and claw-free graphs [5,6]. Providing a decent linear description of the stable set polytopes of claw-free graphs is a longstanding problem [7]. 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 ≤ 3 have rank facets only [3,13] while there are examples with clique number > 4 having non-rank facets [8,10,9]. The aim of the present paper is to treat the remaining case with clique number = 4: we provide an infinite sequence of such webs whose stable set polytopes admit non-rank facets.