A characterization of partially dual graphs

TL;DR

This paper extends the concept of partial duality from ribbon graphs to general graphs, providing a combinatorial characterization based on edge set bijections, generalizing Edmonds' classical duality result.

Contribution

It introduces a new characterization of partial duality for graphs using bijections between edge sets, broadening the understanding of graph duality.

Findings

Characterizes partial duality via edge set bijections

Generalizes Edmonds' duality theorem to partial duality

Provides a combinatorial framework for understanding partial dual graphs

Abstract

In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result generalizes a well known result of J. Edmonds in which natural duality of graphs is characterized in terms of edge correspondence, and gives a combinatorial characterization of partial duality.