10 problems

Sharp series-parallel bound conjecture. Every chromatic root $z$ of $G$ lies in the disc

Series-parallel chromatic-root bound. There exists a universal constant $C<\infty$ such that, for every series-parallel graph $G$ of maximum degree $k$, every chromatic root $z$ li…

Let $G$ be a series-parallel graph, and let $P_G(q)$ be its chromatic polynomial. Write $p$ for the relevant graph parameter in the proposed $p/\log p$ bound, and distinguish maxim…

Let $\mathcal S$ be the class of series-parallel graphs. Biro, Collado and Zamora's conjecture. … The indeque ratio measures the asymptotic minimum proportion of vertices that can…

Let $G$ be a series-parallel graph with maximum degree $\Delta$. A proper coloring is equitable when its color classes differ in size by at most one. Zhang–Wu's conjecture. If…

NP-hardness conjecture. Minimum Eternal Vertex Cover is NP-hard on series-parallel graphs.

Locally series-parallel graph characterization conjecture. The following are equivalent:

Let $\Delta_0$ be the threshold parameter in Theorem, concerning the accumulation of chromatic zeros of leaf joined trees relative to the degree bound $\Delta$. The degree-three th…

Let $B_{5/27}(1)$ denote the disk of radius $5/27$ centered at $1$, and let $Z(G;q)$ be the chromatic polynomial of a series-parallel graph $G$. The punctured-disk zero-free conjec…

Let $G$ be a graph. A spanning tree is a set of edges inducing a connected spanning subgraph without a cycle; write $\tau(G)$ for the number of spanning trees. An acyclic orientati…