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Regularity in tournaments

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Book cover Theory and Applications of Graphs

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 642))

Abstract

A nearly triply regular (abbreviated NTR) tournament is a doubly regular tournament in which every triple of distinct vertices dominates exactly j1 or j2 vertices, where 0 ≤ j1 < j2. We show that if T is NTR and if the outset of a pair of distinct vertices of T either is a singleton or spans a subtournament which is not strongly connected, then j1=0 and j2=1 and T is one of the quadratic residue tournaments of orders 7 or 11.

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References

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Author information

Authors and Affiliations

  1. The Australian National University, Canberra, ACT, 2600, Australia

    Marcel Herzog

  2. Louisiana State University, Baton Rouge, LA, 70803, USA

    K. B. Reid

Authors
  1. Marcel Herzog
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  2. K. B. Reid
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Western Michigan University, Kalamazoo, MI, 49008, USA

    Yousef Alavi  & Don R. Lick  & 

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© 1978 Springer-Verlag Berlin Heidelberg

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Herzog, M., Reid, K.B. (1978). Regularity in tournaments. In: Alavi, Y., Lick, D.R. (eds) Theory and Applications of Graphs. Lecture Notes in Mathematics, vol 642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0070401

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  • DOI: https://doi.org/10.1007/BFb0070401

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08666-6

  • Online ISBN: 978-3-540-35912-8

  • eBook Packages: Springer Book Archive

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