Pseudo 2-factor isomorphic regular bipartite graphs

Authors:
M. Abreu;A. A. Diwan;Bill Jackson;D. Labbate;J. Sheehan
Affiliations:
Dipartimento di Matematica, Università della Basilicata, C. da Macchia Romana, 85100 Potenza, Italy;Department of Computer Science and Engineering, Indian Institute of Technology, Mumbai 400076, India;School of Mathematical Sciences, Queen Mary College, London E1 4NS, UK;Dipartimento di Matematica, Politecnico di Bari, I-70125 Bari, Italy;Department of Mathematical Sciences, King's College, Old Aberdeen AB24 3UE, UK
Venue:
Journal of Combinatorial Theory Series B
Year:
2008

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Abstract

A graph G is pseudo 2-factor isomorphic if the parity of the number of circuits in a 2-factor is the same for all 2-factors of G. We prove that there exist no pseudo 2-factor isomorphic k-regular bipartite graphs for k=4. We also propose a characterization for 3-edge-connected pseudo 2-factor isomorphic cubic bipartite graphs and obtain some partial results towards our conjecture.