7 problems

Perfect-contractility conjecture. The following conditions are equivalent:

Stable-set ideal conjecture. The following conditions are equivalent:

Let $C_n$ be the cycle graph on $n$ vertices, let $p(C_n;z)$ denote its perfectly matchable set polynomial, and let $\overline{h}^*(C_n;z)$ denote the normalized $h^*$-polynomial o…

Let $G$ be a cycle graph with $\ell\geq 3$, let $R=E_{\mathbb{K}}[\operatorname{STAB}(G)]$ be its Ehrhart ring, and write its h-vector as $(h_0,h_1,\ldots,h_s)$ with $h_s\neq 0$. S…

$N_+$-Perfect Graph Conjecture. The stable set polytope of every $N_+$-perfect graph can be described by facet-defining inequalities with near-bipartite support.

Let ${\operatorname{LS}}_+(G)$ denote the Lovász–Schrijver positive semidefinite relaxation of the stable set polytope. A graph is ${\operatorname{LS}}_+$-perfect when…

For a graph $G$, let $\operatorname{STAB}(G)$ be its stable set polytope, $\operatorname{NB}(G)$ the near-bipartite polyhedral relaxation, and ${\operatorname{LS}}_+(G)$ the Lovász…