Eulerian and Even-Face Graph Partial Duals

Abstract

Eulerian and bipartite graph is a dual symmetric concept in Graph theory. It is well-known that a plane graph is Eulerian if and only if its geometric dual is bipartite. In this paper, we generalize the well-known result to embedded graphs and partial duals of cellularly embedded graphs, and characterize Eulerian and even-face graph partial duals of a cellularly embedded graph by means of half-edge orientations of its medial graph.