A construction for non-rank facets of stable set polytopes of webs

Graphs with circular symmetry, called webs, are relevant w.r.t. describing the stable set polytopes of two larger graph classes, quasi-line graphs [9,14] and claw-free graphs [8,9]. Providing a decent linear description of the stable set polytopes of claw-free graphs is a long-standing problem [10]. 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 [6,18] while there are examples with clique number ≥ 4 having non-rank facets [11,12,14,16]. In this paper, we provide a construction for non-rank facets of stable set polytopes of webs. This construction is the main tool to obtain in a companion paper [17], for all fixed values of ω ≥ 5 that there are only finitely many webs with clique number ω whose stable set polytopes admit rank facets only.