Arthur Hobbs, (Texas A&M University)
William T. Tutte, 1917--2002
William T. Tutte's first mathematical research was completed while he
was an undergraduate chemistry major at Cambridge. He and his colleagues,
Brooks, Smith, and Stone, gave the first theory-driven solution to the
problem of covering a square of integer side length with non-overlapping
squares of all-different integer side lengths. Tutte spent the war years
at Bletchley Park, where he almost single-handedly broke the German Army
High Command code (not the Enigma code).
Tutte's 417 page thesis, written at Cambridge during the 3 years
immediately following the war, solved the then most important problem in
matroid theory - characterizing those matroids that can be derived from
graphs - using exclusion of minors introduced by Wagner for graphs. In
his thesis, he also introduced the polynomial now named after him. The
Tutte polynomial subsumes the chromatic polynomial, the tree counting
polynomial, and the flow polynomial, and it has applications in knot
theory and elsewhere.
Tutte continued his career with further extraordinary results. He did
foundational work in several branches of graph theory, including
characterizing graphs with 1-factors, enumerating graphs, advancing the
theory of chromatic polynomials, and characterizing classes of graphs with
Hamiltonian cycles. Tutte was made a Fellow of the Royal Society of
Canada in 1958, a Fellow of the Royal Society in 1987, and an Officer of
the Order of Canada in 2001.
In the March, 2004, issue of the AMS Notices, James Oxley (Louisiana
State University) and the speaker, Arthur Hobbs (Texas A&M University),
published an article on the life and work of William T. Tutte. In the
present talk, Prof. Hobbs will give a more extended review of some of the
more interesting aspects of Tutte's work and life.