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A thousand million leagues

Published online by Cambridge University Press:  01 August 2016

Tony Barnard
Tony Barnard*
Affiliation:
King’s College, The Strand, London WC2R 2LS
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Extract

Some time ago a friend, who was organising a chess league, rang me up and asked “How many different ways are there of arranging a roundrobin league tournament?” Thinking of his phone bill I told him I’d ring him back. Which was just as well, because the problem was much more difficult dian I had realised. Indeed it is unsolved in general. In the language of graph theory it is the problem of finding the number of onefactorisations of a complete graph. These and related objects have been the focus of considerable study both in combinatorics and recreational mathematics and, although the enumeration question remains unanswered in general, it is, even for small numbers of players, remarkably full of interest.

Type
Research Article
Information
The Mathematical Gazette , Volume 77 , Issue 480 , November 1993 , pp. 329 - 336
Copyright
Copyright © The Mathematical Association 1993

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