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On multipartite tournaments. (English) Zbl 0736.05040

The authors derive various results on multipartite tournaments \(T\) concerning (a) the lengths of cycles in \(T\) and (b) the distances from a vertex of maximum score in a given partite set to other vertices within the same partite set.

MSC:

05C20 Directed graphs (digraphs), tournaments
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References:

[1] Bagga, K. S., On upsets in bipartite tournaments, (Alavi, Y.; Chartrand, G.; Goldsmith, D.; Lesniak, L.; Lick, D. R.; Wall, C. E., Graph Theory and its Applications to Algorithms and Computer Science (1985), Wiley: Wiley New York), 37-45 · Zbl 0569.05026
[2] Bagga, K. S.; Beineke, L. W., Some results on binary matrices obtained via bipartite tournaments, (Alavi, Y.; Chartrand, G.; Goldsmith, D.; Lesniak, L.; Lick, D. R.; Wall, C. E., Graph Theory and its Applications to Algorithms and Computer Science (1985), Wiley: Wiley New York), 47-55 · Zbl 0569.05027
[3] Bagga, K. S.; Beineke, L. W., On superstrong bipartite tournaments, (Congr. Numer., 53 (1986)), 113-119 · Zbl 0633.05031
[4] Bagga, K. S.; Beineke, L. W., On the numbers of some subtournaments of a bipartite tournaments, (Proceedings of Third New York Conference on Combinatorial Mathematics. Proceedings of Third New York Conference on Combinatorial Mathematics, Ann. New York Acad. Sci. (1989)), 21-29, No. 555
[5] Bagga, K. S.; Beineke, L. W., Uniquely realizable score lists in bipartite tournaments, Czech. Math. J., 37, 323-333 (1987) · Zbl 0626.05019
[6] Beineke, L. W., A tour through tournaments or bipartite and ordinary tournaments: A comparative survey, (Combinatorics. Combinatorics, London Math. Soc. Lecture Note Ser., Vol. 52 (1981), Cambridge Univ. Press: Cambridge Univ. Press Cambridge, MA), 41-55 · Zbl 0458.05036
[7] Beineke, L. W.; Bagga, K. S., On superstrong tournaments and their scores, (Proceedings of Third New York Conference on Combinatorial Mathematics. Proceedings of Third New York Conference on Combinatorial Mathematics, Ann. New York Acad. of Sci. (1989)), 32-39, No. 555 · Zbl 0707.05030
[8] Beineke, L. W.; Little, C. H.C, Cycles in bipartite tournaments, J. Combin. Theory Ser. B, 32, 140-145 (1982) · Zbl 0465.05035
[9] Beineke, L. W.; Moon, J. W., On bipartite tournaments and scores, (Alavi, Y.; Chartrand, G.; Goldsmith, D.; Lesniak, L.; Lick, D. R., The Theory and Applications of Graphs (1981), Wiley: Wiley New York), 55-71 · Zbl 0473.05031
[10] Camion, P., Chemins et circuits hamiltoniens des graphes complets, C. R. Acad. Sci. Paris Sér. A, 249, 2151-2152 (1959) · Zbl 0092.15801
[11] Chartrand, G.; Lesniak, L., (Graphs & Digraphs (1986), Wadsworth & Brooks/Cole: Wadsworth & Brooks/Cole Monterey, CA) · Zbl 0666.05001
[12] Harary, F.; Moser, L., The theory of round robin tournaments, Amer. Math. Monthly, 73, 231-246 (1966) · Zbl 0142.41602
[13] Moon, J. W., (Topics on Tournaments (1968), Holt, Rinehart, and Winston: Holt, Rinehart, and Winston New York) · Zbl 0191.22701
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