11 problems

Let $G$ be a graph of genus $g$, and let $c(G)$ denote its cop number. Mohar's conjecture. The cop number satisfies … This conjecture proposes the asymptotic growth of cop number i…

Schröder's conjecture. If $G$ has genus $g$, then

Let $G$ be a planar graph, and let $c_k(G)$ denote the smallest number of cops that guarantee capture of the robber when at most $k$ cops may change their positions at each turn. Y…

Hypergraph Meyniel conjecture. The cop number satisfies

Additive tightness conjecture. All six presented upper bounds are tight up to small additive constants.

Crytser–Komarov–Mackey conjecture. For every connected graph $G$ we have

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 $G$ be a graph with no induced subgraph isomorphic to two disjoint edges, and let $cop(G)$ denote its cop number. Sivaraman and Testa's conjecture. The class of $2K_2$-free gra…

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…