M-alternating paths in n-extendable bipartite graphs

Authors:
R. E. L. Aldred;D. A. Holton;Dingjun Lou;Akira Saito
Affiliations:
Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin, New Zealand;Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin, New Zealand;Department of Computer Science, Zhongshan University, Guangzhou 510275, People's Republic of China;Department of Mathematics, Nihon University, Tokyo 156, Japan
Venue:
Discrete Mathematics
Year:
2003

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Abstract

Let G be a bipartite graph with bipartition (X,Y) which has a perfect matching. It is proved that G is n-extendable if and only if for any perfect matching M of G and for each pair of vertices x in X and y in Y there are n internally disjoint M-alternating paths connecting x and y. Furthermore, these n paths start and end with edges in E(G)\M. This theorem is then generalized.