Document Type

Journal Article

Department/Unit

Department of Mathematics

Abstract

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.

Publication Year

2003

Journal Title

Discrete Applied Mathematics

Volume number

130

Issue number

3

Publisher

Elsevier

First Page (page number)

469

Last Page (page number)

485

Referreed

1

DOI

10.1016/S0166-218X(03)00184-7

ISSN (print)

0166218X

Keywords

Perfect matching, Strongly connected orientation, Eulerian orientation, Ear decomposition, In-tree, Rotation graph, Plane graph

Included in

Mathematics Commons

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