Cycle-pancyclism in bipartite tournaments I

Hortensia Galeana-Sánchez

Discussiones Mathematicae Graph Theory (2004)

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

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 ( 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.

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
  2. [2] L.W. Beineke, A tour through tournaments or bipartite and ordinary tournaments: A comparative survey, J. London Math. Soc., Lect. Notes Ser. 52 (1981) 41-55. 
  3. [3] L.W. Beineke and V. Little, Cycles in bipartite tournaments, J. Combin. Theory (B) 32 (1982) 140-145, doi: 10.1016/0095-8956(82)90029-6. Zbl0465.05035
  4. [4] C. Berge, Graphs and Hypergraphs (North-Holland, Amsterdam, 1976). 
  5. [5] J.C. Bermond and C. Thomasen, Cycles in digraphs - A survey, J. Graph Theory 5 (43) (1981) 145-147. 
  6. [6] H. Galeana-Sánchez and S. Rajsbaum, Cycle-Pancyclism in Tournaments I, Graphs and Combin. 11 (1995) 233-243, doi: 10.1007/BF01793009. Zbl0833.05039
  7. [7] H. Galeana-Sánchez and S. Rajsbaum, Cycle-Pancyclism in Tournaments II, Graphs and Combin. 12 (1996) 9-16, doi: 10.1007/BF01858440. Zbl0844.05047
  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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