2 problems

Let $L_n=P_2\times P_n$ be the ladder graph of order $2n$. A graph is prime when its vertices can be bijectively labeled by $\{1,2,\ldots,m\}$, where $m$ is its order, so that adja…

Let $L_k$ denote the ladder with $k$ rungs, namely the $2\times k$ grid graph. A graph contains a union of vertex-disjoint copies of $L_k$ as a minor if it contains such a minor mo…