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

Part of the Lecture Notes in Mathematics book series (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.

Keywords

  • Hamiltonian Cycle
  • Hamiltonian Path
  • Color Color
  • Monochromatic Path
  • Vertex Disjoint Cycle

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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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

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