5 problems

Let $K_n$ be the complete graph on $n$ vertices, let $g_{K_n}(t)$ denote its Speyer polynomial, and let $g'_{K_{n-1}}(t)$ denote the derivative of $g_{K_{n-1}}(t)$ with respect to…

For $n\geq 5$, let $C^n_{1,2}$ be the circulant graph obtained from the cycle on $n$ vertices by adding the edges joining each vertex to the vertex two steps away, with indices tak…

For integers $n\geq 1$ and $k$, let $C^n_{1,k}$ be the graph on vertices identified with $\{1,\ldots,n\}$, obtained from the cycle by adding the edges $\{i,i+k\}$, with vertex labe…

A graph $G$ is 3-connected if it remains connected after the deletion of any set of at most two vertices, and it is planar if it can be drawn in the plane without edge crossings. L…

Let $\mathsf{M}$ be a matroid, and let $g_{\mathsf{M}}(t)$ denote its $g$-polynomial. g-polynomial positivity conjecture. The polynomial $g_{\mathsf{M}}(t)$ has positive coefficien…