Brian Alspach

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Brian Alspach (born May 29, 1938 in North Dakota ) is an American mathematician who deals with graph theory and also with the mathematics of the game of poker .


Alspach grew up in Seattle , where his family moved when he was nine years old. He graduated from the University of Washington with a bachelor's degree in 1961, taught a year in high school, and continued his studies at the University of California, Santa Barbara , where he received his master's degree in 1964 and with Paul J in 1966 Kelly received her PhD (A class of tournaments). Then he was at Simon Fraser University until his retirement in 1998 , where he was professor of mathematics and statistics. Then he was adjunct professor at the University of Regina , where his wife, the mathematician Katherine Heinrich , also has a high position in the university administration. He also teaches at the University of Newcastle in Australia.

He started a degree in industrial mathematics at Simon Fraser University and is interested in the application of graph theory in business administration.

A conjecture named after him from 1981 concerns the decomposition of a complete graph into disjoint cycles of prescribed length. In 2001 he and Heather Gavlas proved the special case of decomposition into cycles of equal length. According to this, such a decomposition is possible if the number of nodes is odd and the cycle length is at most as large as the number of nodes and the cycle length divides the number of nodes. In 2014, the presumption was fully proven.

He published regularly about poker in Poker Digest and Canadian Poker Player .

In 2014 he received the Euler Medal .

Fonts (selection)

  • Cycles of each length in regular tournaments , Canadian Mathematical Bulletin, Volume 10, 1967, pp. 283-286
  • Point-symmetric graphs and digraphs of prime order and transitive permutation groups of prime degree , Journal of Combinatorial Theory, Series B, Volume 15, 1973, pp. 12-17
  • with TD Parsons: Isomorphism of circulant graphs and digraphs , Discrete Mathematics, Volume 25, 1979, pp. 97-108
  • with TD Parsons: A construction for vertex -transitive graph , Canadian Journal of Mathematics, Volume 34, 1982, pp. 307-318
  • Heather Gavlas: Cycle Decompositions of Kn and Kn-I . Journal of Combinatorial Theory, Series B, Volume 81, 2001, pp. 77-99
  • with Marni Mishna: Enumeration of Cayley graphs and digraphs , Discrete Math., Volume 256, 2002, pp. 527-539.
  • Cayley Graphs , in: J. Gross, J. Yellen, Handbook of Graph Theory, CRC Press 2004


  • Joy Morris, Mateja Šajna: Brian Alspach and his work , Discrete Mathematics, Volume 2005, pp. 269–287. pdf

Web links

Individual evidence

  1. Brian Alspach in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ^ University of Newcastle, Brian Alspach
  3. Darryn Bryant, Daniel Horsley, William Pettersson: Cycle decompositions V: Complete graphs into cycles of arbitrary lengths, Proceedings of the London Mathematical Society, Volume 108, 2014, pp. 1153-1192.
  4. Alspach, article in Poker Digest , from his homepage