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2004 | 24 | 2 | 277-290
Tytuł artykułu

Cycle-pancyclism in bipartite tournaments I

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Wydawca
Rocznik
Tom
24
Numer
2
Strony
277-290
Opis fizyczny
Daty
wydano
2004
Twórcy
  • Instituto de Matemáticas, UNAM, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510, México, D.F., MEXICO
Bibliografia
  • [1] B. Alpach, Cycles of each length in regular tournaments, Canad. Math. Bull. 10 (1967) 283-286, doi: 10.4153/CMB-1967-028-6.
  • [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] 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.
  • [4] C. Berge, Graphs and Hypergraphs (North-Holland, Amsterdam, 1976).
  • [5] J.C. Bermond and C. Thomasen, Cycles in digraphs - A survey, J. Graph Theory 5 (43) (1981) 145-147.
  • [6] H. Galeana-Sánchez and S. Rajsbaum, Cycle-Pancyclism in Tournaments I, Graphs and Combin. 11 (1995) 233-243, doi: 10.1007/BF01793009.
  • [7] H. Galeana-Sánchez and S. Rajsbaum, Cycle-Pancyclism in Tournaments II, Graphs and Combin. 12 (1996) 9-16, doi: 10.1007/BF01858440.
  • [8] H. Galeana-Sánchez and S. Rajsbaum, Cycle-Pancyclism in Tournaments III, Graphs and Combin. 13 (1997) 57-63, doi: 10.1007/BF01202236.
  • [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.
  • [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.
  • [11] R. Häggkvist and Y. Manoussakis, Cycles and paths in bipartite tournaments with spanning configurations, Combinatorica 9 (1989) 33-38, doi: 10.1007/BF02122681.
  • [12] L. Volkmann, Cycles in multipartite tournaments, results and problems, Discrete Math. 245 (2002) 19-53, doi: 10.1016/S0012-365X(01)00419-8.
  • [13] C.Q. Zhang, Vertex even-pancyclicity in bipartite tournaments, J. Nanjing Univ. Math., Biquart 1 (1981) 85-88.
  • [14] K.M. Zhang and Z.M. Song, Cycles in digraphs, a survey, J. Nanjing Univ., Nat. Sci. Ed. 27 (1991) 188-215.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1231
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