2 problems

For a finite simple graph $G$, let $L(G)$ denote its line graph, let $G^2$ denote the graph in which two vertices are adjacent exactly when they are at distance at most two in $G$,…

Let $G$ be a finite simple graph. For a non-empty subgraph $H$ of $G$, define its Ore-degree in $G$ by … with $\sigma_G(H)=0$ when $H$ is empty. Suppose that $H$ is a bipartite sub…