Department of Mathematics
The cell rotation graph D(G) on the strongly connected orientations of a 2-edge-connected plane graph G is defined. It is shown that D(G) is a directed forest and every component is an in-tree with one root; if T is a component of D(G), the reversions of all orientations in T induce a component of D(G), denoted by T−, thus (T,T−) is called a pair of in-trees of D(G); G is Eulerian if and only if D(G) has an odd number of components (all Eulerian orientations of G induce the same component of D(G)); the width and height of Tare equal to that of T−, respectively. Further it is shown that the pair of directed tree structures on the perfect matchings of a plane elementary bipartite graph G coincide with a pair of in-trees of D(G). Accordingly, such a pair of in-trees on the perfect matchings of any plane bipartite graph have the same width and height.
Discrete Applied Mathematics
First Page (page number)
Last Page (page number)
Perfect matching, Strongly connected orientation, Eulerian orientation, Ear decomposition, In-tree, Rotation graph, Plane graph
Zhang, Heping, Peter Che Bor Lam, and Wai Chee Shiu. "Cell rotation graphs of strongly connected orientations of plane graphs with an application." Discrete Applied Mathematics 130.3 (2003): 469-485.