Round-Robin Tournaments with homogenous rounds

Bregje Buiteveld, Erik van Holland, Gerhard F. Post, Dirk Smit

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Abstract

We study round-robin tournaments for n teams, where in each round a fixed number (g) of teams is present and each team present plays a fixed number (m) of matches in this round. In the tournament each match between two teams is either played once or twice, in the latter case in different rounds. We give necessary combinatorial conditions on the triples (n, g,m) for which such round-robin tournaments can exist, and discuss three general construction methods that concern the cases m = 1, m = 2 and m = g−1. For n <= 20 these cases cover 149 of all 173 non-trivial cases that satisfy the necessary conditions. Of these 149 cases a tournament can be constructed in 147 cases. For the remaining 24 cases the tournament does not exist in 2 cases, and is constructed in all other cases. Finally we consider the spreading of rounds for teams, and give some examples where well-spreading is either possible or impossible.
Original languageUndefined
Title of host publicationProceedings of the 8th International Conference on the Practice and Theory of Automated Timetabling, PATAT 2010
Place of PublicationBelfast
PublisherQueen's University of Belfast
Pages122-135
Number of pages14
ISBN (Print)08-538-9973-3
Publication statusPublished - 10 Aug 2010
Event8th International Conference on the Practice and Theory of Automated Timetabling, PATAT 2010 - Belfast, United Kingdom
Duration: 10 Aug 201013 Aug 2010
Conference number: 8
http://www.patatconference.org/patat2010/proceedings.html

Publication series

Name
PublisherQueen’s University

Conference

Conference8th International Conference on the Practice and Theory of Automated Timetabling, PATAT 2010
Abbreviated titlePATAT 2010
CountryUnited Kingdom
CityBelfast
Period10/08/1013/08/10
Internet address

Keywords

  • METIS-276183
  • MSC-00A05
  • EWI-18972
  • IR-75074

Cite this

Buiteveld, B., van Holland, E., Post, G. F., & Smit, D. (2010). Round-Robin Tournaments with homogenous rounds. In Proceedings of the 8th International Conference on the Practice and Theory of Automated Timetabling, PATAT 2010 (pp. 122-135). Belfast: Queen's University of Belfast.