8 problems

Let $G$ be a 2-connected graph and let $ij$ be any edge of $G$. Let $\Gamma$ be a unimodular triangulation of the subcomplex of $P_{G\setminus ij}$ consisting of all facets visible…

Summed edge-deletion nonnegativity conjecture. The polynomial $Z_G(t)$ has nonnegative coefficients. This is proposed as a stronger statement whose gamma-nonnegativity would imply…

Let $G$ be a 2-connected graph with edge set $E$, and let $P_G$ denote its symmetric edge polytope. For an edge $e\in E$, let $P_{G\setminus e}$ be the symmetric edge polytope of t…

Cross-degree and interlacing conjecture. The inequalities

Higashitani–Kummer–Michałek conjecture. (i) For any complete multipartite graph $K_{a_1,\dots,a_k}$, the roots of $E_{a_1,\dots,a_k}$ lie on $\operatorname{CL}$. (ii) If…

Let $G$ be a connected graph with $n\geq 3$ vertices. Let ${\mathcal P}_G$ be its symmetric edge polytope, and let $N({\mathcal P}_G)$ denote the number of its facets. A $1$-sum of…

Gamma-zero characterization conjecture. If $k\in\mathbb{N}$ and $G$ is a $k$-connected graph on $n$ vertices, then

Ohsugi–Tsuchiya conjecture. For every $i\geq 0$,