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.
Perfect matching, Strongly connected orientation, Eulerian orientation, Ear decomposition, In-tree, Rotation graph, Plane graph
Source Publication Title
Discrete Applied Mathematics
Link to Publisher's Edition
Zhang, H., Lam, P., & Shiu, W. (2003). Cell rotation graphs of strongly connected orientations of plane graphs with an application. Discrete Applied Mathematics, 130 (3). https://doi.org/10.1016/S0166-218X(03)00184-7