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Monochromatic reachability, complementary cycles, and single arc reversals in tournaments

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Graph Theory Singapore 1983

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1073))

Abstract

Three recent results on tournaments are presented. A direct proof is given of the following consequence of a theorem due to B. Sands, N. Sauer, and R. Woodrow [7] : if the arcs of a tournament are two-colored, then there exists some vertex which is reachable from every other vertex via a monochromatic path. Next, as illustrative of the proof of a more technical result, it is shown that with one exception every 3-connected tournament contains two complementary cycles. And, Ádám's Conjecture is established for 2-arc-connected tournaments which are not 3-arc-connected.

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References

  1. A. Ádám, Problem No.2. Theory of Graphs and its Applications, Proc. Symp., Smolenice, 1963, Academic Press, New York (1964), 157.

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  6. K. B. Reid, Two complementary cycles in two-connected tournaments, in Cycles in Graphs, a volume in the Annals of Discrete Mathematics, North-Holland, to appear.

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  7. B. Sands, N. Sauer, and R. Woodrow, On monochromatic paths in edge-coloured digraphs, J. Comb. Theory Ser. B 33 (1982), 271–275.

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Authors and Affiliations

  1. Louisiana State University, 70803, Baton Rouge, Louisiana, U.S.A.

    K. B. Reid

Authors
  1. K. B. Reid
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Editor information

Khee Meng Koh Hian Poh Yap

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© 1984 Springer-Verlag

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Reid, K.B. (1984). Monochromatic reachability, complementary cycles, and single arc reversals in tournaments. In: Koh, K.M., Yap, H.P. (eds) Graph Theory Singapore 1983. Lecture Notes in Mathematics, vol 1073. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073101

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  • DOI: https://doi.org/10.1007/BFb0073101

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13368-1

  • Online ISBN: 978-3-540-38924-8

  • eBook Packages: Springer Book Archive

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