# Cycle-pancyclism in bipartite tournaments I

• Volume: 24, Issue: 2, page 277-290
• ISSN: 2083-5892

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## Abstract

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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 ${C}_{h\left(k\right)}$ of length h(k), h(k) ∈ k,k-2 with $|A\left({C}_{h\left(k\right)}\right)\cap A\left(\gamma \right)|\ge h\left(k\right)-3$ 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.

## How to cite

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Hortensia Galeana-Sánchez. "Cycle-pancyclism in bipartite tournaments I." Discussiones Mathematicae Graph Theory 24.2 (2004): 277-290. <http://eudml.org/doc/270672>.

@article{HortensiaGaleana2004,
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.},
author = {Hortensia Galeana-Sánchez},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {bipartite tournament; pancyclism},
language = {eng},
number = {2},
pages = {277-290},
title = {Cycle-pancyclism in bipartite tournaments I},
url = {http://eudml.org/doc/270672},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Hortensia Galeana-Sánchez
TI - Cycle-pancyclism in bipartite tournaments I
JO - Discussiones Mathematicae Graph Theory
PY - 2004
VL - 24
IS - 2
SP - 277
EP - 290
AB - 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.
LA - eng
KW - bipartite tournament; pancyclism
UR - http://eudml.org/doc/270672
ER -

## References

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1. [1] B. Alpach, Cycles of each length in regular tournaments, Canad. Math. Bull. 10 (1967) 283-286, doi: 10.4153/CMB-1967-028-6. Zbl0148.43602
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8. [8] H. Galeana-Sánchez and S. Rajsbaum, Cycle-Pancyclism in Tournaments III, Graphs and Combin. 13 (1997) 57-63, doi: 10.1007/BF01202236. Zbl0868.05028
9. [9] H. Galeana-Sánchez and S. Rajsbaum, A Conjecture on Cycle-Pancyclism in Tournaments, Discuss. Math. Graph Theory 18 (1998) 243-251, doi: 10.7151/dmgt.1080. Zbl0928.05031
10. [10] G. Gutin, Cycles and paths in semicomplete multipartite digraphs, theorems and algorithms: A survey, J. Graph Theory 19 (1995) 481-505, doi: 10.1002/jgt.3190190405. Zbl0839.05043
11. [11] R. Häggkvist and Y. Manoussakis, Cycles and paths in bipartite tournaments with spanning configurations, Combinatorica 9 (1989) 33-38, doi: 10.1007/BF02122681. Zbl0681.05036
12. [12] L. Volkmann, Cycles in multipartite tournaments, results and problems, Discrete Math. 245 (2002) 19-53, doi: 10.1016/S0012-365X(01)00419-8. Zbl0996.05063
13. [13] C.Q. Zhang, Vertex even-pancyclicity in bipartite tournaments, J. Nanjing Univ. Math., Biquart 1 (1981) 85-88.
14. [14] K.M. Zhang and Z.M. Song, Cycles in digraphs, a survey, J. Nanjing Univ., Nat. Sci. Ed. 27 (1991) 188-215. Zbl0762.05064

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