2 problems

Let $P_m$ be the path graph on $m$ vertices, let $C_n$ be the cycle graph on $n$ vertices, and let $P_m\Box C_n$ denote their Cartesian product. Write $\gamma(P_m\Box C_n)$ for its…

Linear disjoint-edge conjecture. Every complete monotone simple cylindrical graph contains at least $cn$ pairwise disjoint edges, for some fixed constant $c$.