Round-Robin Tournaments with homogenous rounds

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

Round-Robin Tournaments with homogenous rounds

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

Discrete Mathematics and Mathematical Programming

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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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 language	Undefined
Title of host publication	Proceedings of the 8th International Conference on the Practice and Theory of Automated Timetabling, PATAT 2010
Place of Publication	Belfast
Publisher	Queen's University of Belfast
Pages	122-135
Number of pages	14
ISBN (Print)	08-538-9973-3
Publication status	Published - 10 Aug 2010
Event	8th International Conference on the Practice and Theory of Automated Timetabling, PATAT 2010 - Belfast, United Kingdom Duration: 10 Aug 2010 → 13 Aug 2010 Conference number: 8 http://www.patatconference.org/patat2010/proceedings.html

Publication series

Name
Publisher	Queen’s University

Conference

Conference	8th International Conference on the Practice and Theory of Automated Timetabling, PATAT 2010
Abbreviated title	PATAT 2010
Country	United Kingdom
City	Belfast
Period	10/08/10 → 13/08/10
Internet address	http://www.patatconference.org/patat2010/proceedings.html

Keywords

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

Access to Document

PATAT10_Proceedings
open
PATAT10_Proceedings
open

http://www.cs.qub.ac.uk/~B.McCollum/patat10

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.

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title = "Round-Robin Tournaments with homogenous rounds",

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.",

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month = "8",

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isbn = "08-538-9973-3",

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Buiteveld, B, van Holland, E, Post, GF & 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. Queen's University of Belfast, Belfast, pp. 122-135, 8th International Conference on the Practice and Theory of Automated Timetabling, PATAT 2010, Belfast, United Kingdom, 10/08/10.

Round-Robin Tournaments with homogenous rounds. / Buiteveld, Bregje; van Holland, Erik; Post, Gerhard F.; Smit, Dirk.

Proceedings of the 8th International Conference on the Practice and Theory of Automated Timetabling, PATAT 2010. Belfast : Queen's University of Belfast, 2010. p. 122-135.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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N2 - 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.

AB - 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.

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