Graph Models of Harems and Tournaments in Sports Clubs

Mochamad Suyudi

Abstract


By looking at the extension of Hall's marriage theorem to harems, where some people are allowed to have more than one partner, Traditionally in harems any man can have multiple wives but no woman can have more than one husband. then consider the different types of matches by looking at 'round robin tournaments' in sports clubs. An unexpected connection between the two worlds emerged when we were able to use our harem results to deduce theorems about the tournament.


Keywords


Hall's marriage theorem, Hall's theorem - harem form, Landou theorem, tournamen.

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References


Bryant, Victor.(1993). Aspects of combinatorics : a wide-ranging introduction. Cambridge university press.

Landau, H. G.(1953). On dominance relations and the structure of animal societies. III. The condition for a score structure, Bull. Math. Biophys. 15, 143-148.

Reid, K. B.(1996). Tournaments: scores, kings, generalizations and special topics, In: Surveys on Graph Theory (edited by G. Chartrand and M. Jacobson), CongressusNumerantium 115, 171-211.

Thommasen, C. (1981). Landau's characterization of tournament score sequences, In: The Theory and Applications of Graphs (Kalamazoo, Mich., 1980). John Wiley & Sons, 589-591.

Wilson, Robin J. (1996). Introduction to Graph Theory, Fourth edition, Addison Wesley Longman Limited Edinburgh Gate, Harlow, Essex CM20 2JE, England and Associated Companies throughout the world.




DOI: https://doi.org/10.46336/ijqrm.v3i4.378

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IJQRM: Jalan Riung Ampuh No. 3, Riung Bandung, Kota Bandung 40295, Jawa Barat, Indonesia

 

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