The Contributions of W.T. Tutte to Matroid Theory
Bill Tutte was born on May 14, 1917 in Newmarket, England. In 1935, he began studying at Trinity College, Cambridge reading natural sciences specializing in chemistry. After completing a master’s degree in chemistry in 1940, he was recruited to work at Bletchley Park as one of an elite group of codebreakers that included Alan Turing. While there, Tutte performed “one of the greatest intellectual feats of the Second World War.” Returning to Cambridge in 1945, he completed a Ph.D. in mathematics in 1948. Thereafter, he worked in Canada, first in Toronto and then as a founding member of the Department of Combinatorics and Optimization at the University of Waterloo. His contributions to graph theory alone mark him as arguably the twentieth century’s leading researcher in that subject. He also made groundbreaking contributions to matroid theory including proving the first excluded-minor theorems for matroids, one of which generalized Kuratowski’s Theorem. He extended Menger’s Theorem to matroids and laid the foundations for structural matroid theory. In addition, he introduced the Tutte polynomial for graphs and extended it and some relatives to matroids. This paper will highlight some of his many contributions focusing particularly on those to matroid theory.
Unable to display preview. Download preview PDF.
Part of this paper was presented by the second author at the Tutte Centenary Retreat (https://www.matrix-inst.org.au/events/tutte-centenary-retreat/) held at the MAThematical Research Institute (MATRIx), Creswick, Victoria, Australia, 26 Nov. to 2 Dec. 2017. The authors gratefully acknowledge the support of MATRIx for this retreat.
- 1.Ball, W.W.R.: Mathematical Recreations and Essays, 1st edn. Macmillan, London (1892). Revised and updated by H.S.M. Coxeter, 13th edn. Dover, New York (1987)Google Scholar
- 2.BBC 2011: Code-breakers: Bletchley Park’s lost heroes. Documentary (October 2011). Producer/Director Julian CareyGoogle Scholar
- 7.Farr, G.: Remembering Bill Tutte: another brilliant codebreaker from World War II, 12 May 2017. http://theconversation.com/remembering-bill-tutte-another-brilliant-codebreaker-from-world-war-ii-77556
- 9.Farr, G.E., The history of Tutte-Whitney polynomials, with commentary on the classics. In: Ellis-Monaghan, J., Moffatt, I. (eds.) Handbook of the Tutte Polynomial. CRC Press, Boca Raton (to appear)Google Scholar
- 12.Harper, N.: Keeping secrets. University of Waterloo Magazine, Spring, 2015. https://uwaterloo.ca/magazine/spring-2015/features/keeping-secrets Google Scholar
- 13.Hobbs, A.M., Oxley, J.G.: William T. Tutte, 1917–2001. Not. Am. Math. Soc. 51, 320–330 (2004)Google Scholar
- 14.Jaeger, F.: On nowhere-zero flows in multigraphs. In: Nash-Williams, C.St.J.A., Sheehan, J. (eds.) Proceedings of the Fifth British Combinatorial Conference, pp. 373–378. Congressus Numerantium, No. XV. Utilitas Mathematica, Winnipeg (1976)Google Scholar
- 23.Tait, P.G.: Listing’s topologie. Philos. Mag., 5th Series 17, 30–46 (1884)Google Scholar
- 28.Tutte, W.T.: An algebraic theory of graphs. Ph.D. thesis, Cambridge University (1948). https://billtuttememorial.org.uk/links/
- 31.Tutte, W.T.: A homotopy theorem for matroids. I, II. Trans. Am. Math. Soc. 88, 144–174 (1958)Google Scholar
- 32.Tutte, W.T.: Squaring the square. In: Scientific American, Mathematical Games Column (November 1958). Reprinted in Gardner, M.: More Mathematical Puzzles and Diversions. G. Bell and Sons, London (1963) http://www.squaring.net/history_theory/brooks_smith_stone_tutte_II.html
- 35.Tutte, W.T.: How to draw a graph. Proc. Lond. Math. Soc. (3) 13, 743–767 (1963)Google Scholar
- 43.Tutte, W.T.: Projective geometry and the 4-color problem. In: Tutte, W.T. (ed.) Recent Progress in Combinatorics, pp. 199–207. Academic Press, New York (1969)Google Scholar
- 44.Tutte, W.T.: A geometrical version of the four color problem. In: Bose, R.C., Dowling, T.A. (eds.) Combinatorial Mathematics and Its Applications, pp. 553–560. University of North Carolina Press, Chapel Hill (1969)Google Scholar
- 45.Tutte, W.T.: Selected Papers of W. T. Tutte/Edited by D. McCarthy, R. G. Stanton, vol. I. Charles Babbage Research Centre, Winnipeg (1979)Google Scholar
- 46.Tutte, W.T.: Selected Papers of W. T. Tutte/Edited by D. McCarthy, R. G. Stanton, vol. II. Charles Babbage Research Centre, Winnipeg (1979)Google Scholar
- 47.Tutte, W.T.: The coming of the matroids. In: Lamb, J.D., Preece, D.A. (eds.) Surveys in Combinatorics, pp. 3–14. Cambridge University Press, Cambridge (1999)Google Scholar
- 51.Whitney, H.: The coloring of graphs. Ann. Math. (2) 33, 688–718 (1932)Google Scholar