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Discussiones Mathematicae Graph Theory 24(3) (2004) 529-538
DOI: https://doi.org/10.7151/dmgt.1250

CYCLE-PANCYCLISM IN BIPARTITE TOURNAMENTS II

Hortensia Galeana-Sánchez

Instituto de Matemáticas, UNAM
Universidad Nacional Autónoma de México
Ciudad Universitaria
04510, México, D.F. MÉXICO
e-mail: hgaleana@matem.unam.mx

Abstract

Let T be a hamiltonian bipartite tournament with n vertices, γ a hamiltonian directed cycle of T, and k an even number. In this paper the following question is studied: What is the maximum intersection with γ of a directed cycle of length k contained in T[V(γ)]? It is proved that for an even k in the range [(n+6)/2] ≤ k ≤ n−2, there exists a directed cycle C_h(k) of length h(k), h(k) ∈ {k,k−2} with |A(C_h(k))∩A(γ)| ≥ h(k)−4 and the result is best possible. In a previous paper a similar result for 4 ≤ k ≤ [(n+4)/2] was proved.

Keywords: bipartite tournament, pancyclism.

2000 Mathematic Subject Classification: 05C20.

References

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Received 10 September 2003
Revised 30 April 2004