5 problems

Let $X$ be a geodesic surface of genus $g$, and let $c(X)$ denote its cop number. Schroeder's genus conjecture. … The paper compares this conjecture with a linear upper bound and a…

Suppose that $X$ is an $n$-dimensional simplicial pseudomanifold, meaning that each simplex is contained in an $n$-simplex and each $(n-1)$-simplex is contained in at most two $n$-…

Let $G$ and $J$ be connected graphs. Write $G\vee J$ for their graph join, $c_H(X)$ for the hyperopic cop number of a graph $X$, and let $\Upsilon(X)$ denote the maximum size of a…

Subdivided complete-graph conjecture. For every such graph $G$,

Let $c(g)$ denote the maximum cop number of a graph embedded in an orientable surface of genus $g$, and let $\tilde c(g)$ denote the corresponding maximum for graphs embedded in a…