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Discussiones Mathematicae Graph Theory 24(2) (2004) 277-290
DOI: https://doi.org/10.7151/dmgt.1231

CYCLE-PANCYCLISM IN BIPARTITE TOURNAMENTS I

Hortensia Galeana-Sánchez

Instituto de Matemáticas, UNAM
Universidad Nacional Autónoma de México
Ciudad Universitaria, 04510, México, D.F., MEXICO
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? It is proved that for an even k in the range 4 ≤ k ≤ [(n+4)/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)−3 and the result is best possible.

In a forthcoming paper the case of directed cycles of length k, k even and k > [(n+4)/2] will be studied.

Keywords: bipartite tournament, pancyclism.

2000 Mathematics Subject Classification: 05C20.

References

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Received 27 September 2002
Revised 25 September 2003