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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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References

1. Cameron, P.J., Parallelisms of complete designs, London Math. Soc. Lecture Note Ser. 23, C.U.P. (1976). Ch. 4: Edge-colourings of complete graphs.CrossRefGoogle Scholar
2. Cameron, P.J., and Van Lint, J.H., Graphs, codes and designs, London Math. Soc. Lecture Note Ser. 43, C.U.P. (1980). Ch. 8: 1-factorisations of K6.Google Scholar
3. Coxeter, H.S.M., “Twelve points in PG(5,3) with 95040 self-transformations”. Proc. Roy. Soc. Ser. A, 247 (1958) 279–293.Google Scholar
4. Dickson, L.E., and Safford, F.H., “Solution to Problem 8 (Group theory)” Amer. Math. Monthly 13 (1906) 150–151.Google Scholar
5. Gelling, E.N., On 1-factorizations of the complete graph and the relation to round robin schedules, MSc thesis, University of Victoria (1973).Google Scholar
6. Lucas, E., Récréations mathématiques. Vol. 2, Gauthier-Villars, Paris (1883). Sixiéme réécréation: Les jeux de demoiselles, pp161–197.Google Scholar
7. Mendelsohn, E., and Rosa, A., “One factorizations of the complete graph - a survey”, J. Graph Theory 9 (1985) 43–65.Google Scholar
8. Sylvester, J.J., Collected mathematical papers 1, C.U.P. (1904). No. 17: Elementary researches in the analysis of combinatorial aggregation (1844).Google Scholar
9. Sylvester, J.J., Collected mathematical papers 2, C.U.P. (1908). No. 46: Note on the historical origin of the unsymmetrical six-valued function of six letters (1861).Google Scholar
10. Wallis, W.D., Street, A.P., and Wallis, J.S., Combinatorics: Room squares, Sum-free sets, Hadamard matrices, Lecture Notes in Mathematics 292, Springer, Berlin (1972). Chapter VIII: Room squares of side 7.CrossRefGoogle Scholar
11. Wallis, W.D., “One-factorizations of graphs: tournament applications”, College Math. Journal 18 (2) (1987) 116–123.CrossRefGoogle Scholar
12. Wallis, W.D., “A tournament problem”, J. Austral. Math. Soc. Ser. B 24 (1983) 289–291.CrossRefGoogle Scholar