Nontrivial independent sets of bipartite graphs and cross-intersecting families

Jun Wang, Huajun Zhang

Let $G(X,Y)$ be a connected, non-complete bipartite graph with $|X|\le |Y|$. An independent set $A$ of $G(X,Y)$ is said to be trivial if $A\subseteq X$ or $A\subseteq Y$. Otherwis…