Resonance of Plane Bipartite Graphs

Abstract

A graph $G$ is called resonant if the boundary of each face of $G$ is an $F$-alternating closed trail with respect to some $f$-factor $F$ of $G$. We show that a plane bipartite graph $G$ is resonant if and only if it is connected and each edge of $G$ is contained in an $f$-factor and not in another $f$-factor.