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On the Number of Hamiltonian Cycles in Bipartite Graphs

Published online by Cambridge University Press:  12 September 2008

Carsten Thomassen
Carsten Thomassen
Affiliation:
Mathematical Institute, Technical University of Denmark, DK-2800 Lyngby, Denmark
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Abstract

We prove that a bipartite uniquely Hamiltonian graph has a vertex of degree 2 in each color class. As consequences, every bipartite Hamiltonian graph of minimum degree d has at least 21−dd! Hamiltonian cycles, and every bipartite Hamiltonian graph of minimum degree at least 4 and girth g has at least (3/2)g/8 Hamiltonian cycles. We indicate how the existence of more than one Hamiltonian cycle may lead to a general reduction method for Hamiltonian graphs.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 4 , December 1996 , pp. 437 - 442
Copyright
Copyright © Cambridge University Press 1996

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References

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