Peripheral convex expansions of resonance graphs

TL;DR

This paper characterizes when the resonance graph of a plane elementary bipartite graph can be constructed through peripheral convex expansions, linking it to the property of the infinite face being forcing.

Contribution

It provides a necessary and sufficient condition for constructing resonance graphs via peripheral convex expansions based on the forcing property of the infinite face.

Findings

Resonance graph construction characterized by peripheral convex expansions.

Condition established: infinite face being forcing is equivalent to constructibility.

Provides a new method for analyzing resonance graphs in bipartite graphs.

Abstract

In this paper, we show that the resonance graph of a plane elementary bipartite graph $G$ can be obtained from an edge by a sequence of peripheral convex expansions with respect to a reducible face decomposition of $G$ if and only if the infinite face of $G$ is forcing.