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.