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A Seminar on Graph Theory

Frank Harary
Publisher: 
Dover Publications
Publication Date: 
2015
Number of Pages: 
116
Format: 
Paperback
Price: 
12.95
ISBN: 
9780486796840
Category: 
Monograph
[Reviewed by
Tom Schulte
, on
04/29/2016
]

Frank Harary, who edited this collection, was a prolific American mathematician specializing in graph theory. Dover published this book on the decennial of his passing. Harary held a faculty position in the University of Michigan Department of Mathematics from 1948-86 and in 1955 taught UM’s first graph theory and combinatorial theory courses. That department’s obituary recalls Harary as the “father” of modern graph theory, a discipline he helped found and popularize. Colleagues, peers and students fondly referred to Harary as “Mr. Graph Theory.”

A congenial warmth and a sense of humor come across in this two-part collection of expository lectures delivered by experts in the field during 1962–63 at University College, London. Harary’s own lectures make up the first part. The final three of these half-dozen talks focus on work from George Pólya, largely in an area of great interest to Harary: graph enumeration. This is a fast-paced, high-level overview of the state of the art, with proofs mostly omitted entirely as Harary surveys the field for the audience. Of course, this was over a decade before the four color theorem became, in 1976, the first major theorem proved using a computer, so it is described here as an open problem.

Presentations by faculty and visiting scholars in the second part continue to benefit from Harary’s voice due to his light-hearted introductions touching on biography and anecdotes. These eight pieces include three from Paul Erdős and, the largest chapter of the collection, fourteen pages exploring the intersection of graph theory and “composite games" by British statistician and geneticist Cedric A. B. Smith. (In composite games, two players’ singles moves range over a subset of multiple games.) A highlight in this section is J. W. Moon’s overview of multiple proofs of Cayley’s Formula, making it ripe for exposition to and even extension by students.


Tom Schulte exposits on algebra for students of Oakland Community College in Michigan.

The table of contents is not available.