Cycle-pancyclism in bipartite tournaments II
Hortensia Galeana-Sánchez
Discussiones Mathematicae Graph Theory, Tome 24 (2004), p. 529-538 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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 Ch(k) of length h(k), h(k) ∈ k,k-2 with |A(Ch(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.

Publié le : 2004-01-01
EUDML-ID : urn:eudml:doc:270345 
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1250,
     author = {Hortensia Galeana-S\'anchez},
     title = {Cycle-pancyclism in bipartite tournaments II},
     journal = {Discussiones Mathematicae Graph Theory},
     volume = {24},
     year = {2004},
     pages = {529-538},
     zbl = {1063.05061},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1250}
}

Hortensia Galeana-Sánchez. Cycle-pancyclism in bipartite tournaments II. Discussiones Mathematicae Graph Theory, Tome 24 (2004) pp. 529-538. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1250/

[000] [1] B. Alspach, Cycles of each length in regular tournaments, Canadian Math. Bull. 10 (1967) 283-286, doi: 10.4153/CMB-1967-028-6. | Zbl 0148.43602

[001] [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.

[002] [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. | Zbl 0465.05035

[003] [4] C. Berge, Graphs and hypergraphs (North-Holland, Amsterdam, 1976).

[004] [5] J.C. Bermond and C. Thomasen, Cycles in digraphs, A survey, J. Graph Theory 5 (1981) 145-147, doi: 10.1002/jgt.3190050102.

[005] [6] H. Galeana-Sánchez and S. Rajsbaum, Cycle-Pancyclism in Tournaments I, Graphs and Combinatorics 11 (1995) 233-243, doi: 10.1007/BF01793009. | Zbl 0833.05039

[006] [7] H. Galeana-Sánchez and S. Rajsbaum, Cycle-Pancyclism in Tournaments II, Graphs and Combinatorics 12 (1996) 9-16, doi: 10.1007/BF01858440. | Zbl 0844.05047

[007] [8] H. Galeana-Sánchez and S. Rajsbaum, Cycle-Pancyclism in Tournaments III, Graphs and Combinatorics 13 (1997) 57-63, doi: 10.1007/BF01202236. | Zbl 0868.05028

[008] [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. | Zbl 0928.05031

[009] [10] H. Galeana-Sanchez, Cycle-Pancyclism in Bipartite Tournaments I, Discuss. Math. Graph Theory 24 (2004) 277-290, doi: 10.7151/dmgt.1231. | Zbl 1063.05060

[010] [11] 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. | Zbl 0839.05043

[011] [12] R. Häggkvist and Y. Manoussakis, Cycles and paths in bipartite tournaments with spanning configurations, Combinatorica 9 (1989) 33-38, doi: 10.1007/BF02122681. | Zbl 0681.05036

[012] [13] L. Volkmann, Cycles in multipartite tournaments, results and problems, Discrete Math. 245 (2002) 19-53, doi: 10.1016/S0012-365X(01)00419-8. | Zbl 0996.05063

[013] [14] C.Q. Zhang, Vertex even-pancyclicity in bipartite tournaments, J. Nanjing Univ. Math. Biquart 1 (1981) 85-88.

[014] [15] K.M. Zhang and Z.M. Song, Cycles in digraphs, a survey, J. Nanjing Univ., Nat. Sci. Ed. 27 (1991) 188-215. | Zbl 0762.05064