The number of 2-edge-colored complete graphs with unique Hamiltonian alternating cycle

Authors:
A. Benkouar;Y. Manoussakis;R. Saad
Affiliations:
LRI, Bat. 490, 91405 Orsay Cedex, France;LRI, Bat. 490, 91405 Orsay Cedex, France;Laboratoire d'Informatique Fondamentale, Université de Boumerdes, Bat 68 A2, 35000 Boumerdes, Algeria
Venue:
Discrete Mathematics
Year:
2003

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Abstract

Let G be a 2-edge-colored complete graph of even order n. A cycle of G is alternating if any two successive edges differ in color. We prove that there is a one-to-one correspondence between the set of bipartite tournaments of order n admitting a unique Hamiltonian cycle and the set of 2-edge-colored complete graphs of order n admitting a unique alternating Hamiltonian cycle.