Brian Roger Alspach is a

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

whose main research interest is in

graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ...

. Alspach has also studied the mathematics behind

poker Poker is a family of comparing card games in which players wager over which hand is best according to that specific game's rules. It is played worldwide, however in some places the rules may vary. While the earliest known form of the game w ...

, and writes for ''Poker Digest ''and ''Canadian Poker Player'' magazines.

Biography

Brian Alspach was born on May 29, 1938, in

North Dakota North Dakota () is a U.S. state in the Upper Midwest, named after the Native Americans in the United States, indigenous Dakota people, Dakota Sioux. North Dakota is bordered by the Canadian provinces of Saskatchewan and Manitoba to the north a ...

. He attended the

University of Washington The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington. Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seattle a ...

from 1957 to 1961, receiving his B.A. in 1961. He taught at a junior high school for one year before beginning his graduate studies. In 1964 he received his master's degree and in 1966 he obtained his Ph.D. from the

University of California, Santa Barbara The University of California, Santa Barbara (UC Santa Barbara or UCSB) is a Public university, public Land-grant university, land-grant research university in Santa Barbara County, California, Santa Barbara, California with 23,196 undergraduate ...

under the supervision of Paul Kelly. He taught at

Simon Fraser University Simon Fraser University (SFU) is a public research university in British Columbia, Canada, with three campuses, all in Greater Vancouver: Burnaby (main campus), Surrey, and Vancouver. The main Burnaby campus on Burnaby Mountain, located from ...

for 33 years. He retired from there in 1998. He currently works as an adjunct professor at the

University of Regina The University of Regina is a public research university located in Regina, Saskatchewan, Canada. Founded in 1911 as a private denominational high school of the Methodist Church of Canada, it began an association with the University of Saskatchew ...

and has been there since 1999. He is responsible for creating an industrial mathematics degree at

. Brian Alspach believes that the growth and future of mathematics will depend on the business people in the industrial businesses. His interests are in graph theory and its applications. One of his theories of coverings and decomposition has been applied to scheduling issues that can arise in the business world. Alspach states that his biggest issue with this is trying to explain such complex math to people in the business world with only a basic

understanding Understanding is a psychological process related to an abstract or physical object, such as a person, situation, or message whereby one is able to use concepts to model that object. Understanding is a relation between the knower and an object o ...

of math. He has mentored a total of 13 Ph.D. students. His wife is the former vice president of academics at the University of Regina where he was an adjunct professor. Brian is currently employed as conjoint professor at the University of Newcastle.

Research

One of his first publications was an article titled ''Cycles of each length in regular tournaments'', which was published in the

Canadian Mathematical Bulletin The ''Canadian Mathematical Bulletin'' (french: Bulletin Canadien de Mathématiques) is a mathematics journal, established in 1958 and published quarterly by the Canadian Mathematical Society. The current editors-in-chief of the journal are Antoni ...

(November, 1967). Another influential piece of Brian Alspach is ''Point-symmetric graphs and digraphs of prime order and transitive permutation groups of prime degree'', which was published in the

Journal of Combinatorial Theory The ''Journal of Combinatorial Theory'', Series A and Series B, are mathematical journals specializing in combinatorics and related areas. They are published by Elsevier. ''Series A'' is concerned primarily with structures, designs, and applicat ...

(August, 1973). In his article titled ''Isomorphism of circulant graphs and digraphs'' which was published in

Discrete Mathematics Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous f ...

(February, 1979). He discusses the isomorphism problem for a special class of graphs. Brian Alspach coauthored an article with T. D. Parsons titled ''A construction for vertex –transitive graph'' published in the

Canadian Journal of Mathematics The ''Canadian Journal of Mathematics'' (french: Journal canadien de mathématiques) is a bimonthly mathematics journal published by the Canadian Mathematical Society. It was established in 1949 by H. S. M. Coxeter and G. de B. Robinson. The cur ...

(April, 1982).

Alspach's conjecture Alspach's conjecture is a Theorem, mathematical theorem that characterizes the Edge cycle cover, disjoint cycle covers of complete graphs with prescribed cycle lengths. It is named after Brian Alspach, who posed it as a research problem in 1981. A p ...

, posed by Alspach in 1981, concerns the characterization of disjoint cycle covers of

complete graph In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of distinct vertices is c ...

s with prescribed cycle lengths. With Heather Gavlas Jordon, in 2001, Alspach proved a special case, on the decomposition of complete graphs into cycles that all have the same length. This is possible if and only if the complete graph has an odd number of vertices (so its degree is even), the given cycle length is at most the number of vertices (so that cycles of that length exist), and the given length divides the number of edges of the graph. A proof of the full conjecture was published in 2014.

References

External links

Alspach's Mathematics & Poker Page

Graph Theory of Brian Alspach: a conference in celebration of Alspach's 65th birthday

Publications
{{DEFAULTSORT:Alspach, Brian Graph theorists 20th-century American mathematicians 21st-century American mathematicians 1938 births Mathematicians from North Dakota Living people University of Washington alumni University of California, Santa Barbara alumni American emigrants to Canada