4 problems

Let $q_G(x)$ denote the interlace polynomial of a graph $G$. There are constants $c_1,c_2,\ldots$ with … such that, for every $k\geq 1$ and all sufficiently large $n$, there are gr…

Let $G$ be a graph, let $\mathrm{D}(G)$ be its adjacency delta-matroid, and let $\operatorname{Int}_{\mathrm{D}(G)}(v)$ be its interlace polynomial. Interlace-polynomial unimodalit…

LC-orbit minimum-degree conjecture. Then there is no graph on $n$ vertices whose minimum vertex degree among all graphs in its LC orbit is greater than $\delta$. The statement prop…

Let $G$ be a graph and write its interlace polynomial as … The coefficient sequence $(a_1,a_2,\ldots,a_d)$ is called unimodal if it increases to a maximum and then decreases. Arrat…