Cyclability in bipartite graphs

Abstract

Let $G = (X,Y,E)$ be a balanced $2$-connected bipartite graph and $S \subset V(G)$. We will say that $S$ is cyclable in $G$ if all vertices of $S$ belong to a common cycle in $G$. We give sufficient degree conditions in a balanced bipartite graph $G$ and a subset $S \subset V(G)$ for the cyclability of the set $S$.