A characterization of partially 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.

V2: the statement of the main result has been changed. To appear in JGT.

References in corpus (4)

• The Jones polynomial and graphs on surfaces
• The multivariate signed Bollobas-Riordan polynomial
• Knot invariants and the Bollobas-Riordan polynomial of embedded graphs
• Partial duality and Bollobas and Riordan's ribbon graph polynomial

Cited by in corpus (7)

• Separability and the genus of a partial dual
• Bipartite partial duals and circuits in medial graphs
• Partial duals of plane graphs, separability and the graphs of knots
• Non-orientable quasi-trees for the Bollobas-Riordan polynomial
• On a conjecture of Gross, Mansour and Tucker
• On the Seifert graphs of a link diagram and its parallels
• Arrow ribbon graphs