Some cyclic properties of $L_1$-graphs

Jonas B. Granholm

A graph $G$ is called an $L_1$-graph if $d(u)+d(v)\ge |N(u)\cup N(v)\cup N(w)|-1$ for every triple of vertices $u,v,w$ where $u$ and $v$ are at distance 2 and $w\in N(u)\cap N(v)$.…