William G. Brown is a Canadian mathematician specializing 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 ...

. He is a

professor emeritus ''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...

of mathematics at

McGill University McGill University (french: link=no, Université McGill) is an English-language public research university located in Montreal, Quebec, Canada. Founded in 1821 by royal charter granted by King George IV,Frost, Stanley Brice. ''McGill Universit ...

Education and career

Brown earned his Ph.D. from the

University of Toronto The University of Toronto (UToronto or U of T) is a public research university in Toronto, Ontario, Canada, located on the grounds that surround Queen's Park. It was founded by royal charter in 1827 as King's College, the first institution ...

in 1963, under the joint supervision of

Harold Scott MacDonald Coxeter Harold Scott MacDonald "Donald" Coxeter, (9 February 1907 – 31 March 2003) was a British and later also Canadian geometer. He is regarded as one of the greatest geometers of the 20th century. Biography Coxeter was born in Kensington t ...

and

W. T. Tutte William Thomas Tutte OC FRS FRSC (; 14 May 1917 – 2 May 2002) was an English and Canadian codebreaker and mathematician. During the Second World War, he made a brilliant and fundamental advance in cryptanalysis of the Lorenz cipher, a majo ...

. His dissertation was ''Enumeration Problems Of Linear Graph Theory (Problems in the Enumeration of Maps)''. In 1968, he moved to McGill from the

University of British Columbia The University of British Columbia (UBC) is a public university, public research university with campuses near Vancouver and in Kelowna, British Columbia. Established in 1908, it is British Columbia's oldest university. The university ranks a ...

as an associate professor.

Contributions

Brown's dissertation research concerned graph enumeration, and his early publications continued in that direction. However, much of his later work was in extremal graph theory. He is known for formulating the

Ruzsa–Szemerédi problem In combinatorial mathematics and extremal graph theory, the Ruzsa–Szemerédi problem or (6,3)-problem asks for the maximum number of edges in a graph in which every edge belongs to a unique triangle. Equivalently it asks for the maximum number ...

on the density of systems of triples in which no six points contain more than two triples in joint work with

Paul Erdős Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in ...

and

Vera T. Sós Vera T. Sós (born September 11, 1930) is a Hungarian mathematician, specializing in number theory and combinatorics. She was a student and close collaborator of both Paul Erdős and Alfréd Rényi. She also collaborated frequently with her husb ...

, and for his constructions of dense

K_

-free graphs in connection with the

Zarankiewicz problem The Zarankiewicz problem, an unsolved problem in mathematics, asks for the largest possible number of edges in a bipartite graph that has a given number of vertices and has no complete bipartite subgraphs of a given size.. Reprint of 1978 Academi ...

Selected publications

References

External links

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{{DEFAULTSORT:Brown, W. G. Year of birth missing (living people) Living people Canadian mathematicians Graph theorists University of Toronto Academic staff of the University of British Columbia Faculty of Science Academic staff of McGill University