Stable sets in flag spheres

Abstract

We provide lower and upper bounds on the minimum size of a maximum stable set over graphs of flag spheres, as a function of the dimension of the sphere and the number of vertices. Further, we use stable sets to obtain an improved Lower Bound Theorem for the face numbers of flag spheres.

10 pages, 2 figures, to appear at FPSAC2022. Major revision, in particular, Thm.1.3 now claims a weaker lower bound, as in v1 the proof had a gap: we wrongly claimed that a certain sum of ideals is direct. These ideals are irrelevant in the current version