Graph Theory As I Have Known It

by W. T. Tutte

Overview

This book provides a unique and unusual introduction to graph theory by one of the founding fathers, and will be of interest to all researchers in the subject. It is not intended as a comprehensive treatise, but rather as an account of those parts of the theory that have been of special interest to the author. Professor Tutte details his experience in the area, and provides a fascinating insight into how he was led to his theorems and the proofs he used. As well as being of historical interest it provides a useful starting point for research, with references to further suggested books as well as the original papers. The book starts by detailing the first problems worked on by Professor Tutte and his colleagues during his days as an undergraduate member of the Trinity Mathematical Society in Cambridge. It covers subjects such as comnbinatorial problems in chess, the algebraicization of graph theory, reconstruction of graphs, and the chromatic eigenvalues. In each case fascinating historical and biographical information about the author's research is provided.

Product Details

ISBN-13:	9780191637780
Publisher:	Oxford University Press
Publication date:	05/24/2012
Series:	Oxford Lecture Series in Mathematics and Its Applications , #11
Sold by:	Barnes & Noble
Format:	eBook
File size:	20 MB
Note:	This product may take a few minutes to download.

About the Author

William Tutte (1917-2002) studied at Cambridge where his fascination for mathematical puzzles brought him into contact with like-minded undergraduates, together becoming known as the 'Trinity four', the founders of modern graph theory. His notable problem-solving skills meant he was brought to Bletchley Park during World War Two. Key in the enemy codebreaking efforts, he cracked the Lorenz cipher for which the Colossus machine was built, making his contribution comparable to Alan Turing's codebreaking for Enigma. Following his incredible war effort Tutte returned to academia and became a fellow of the Royal Society in Britain and Canada, finishing his career as Distinguished Professor Emeritus at the University of Waterloo, Ontario.

Table of Contents

1. Squaring the square2. Knights errant3. Graphs within graphs4. Unsymmetrical electricity5. Algebra in graph theory6. Symmetry in graphs7. Graphs on spheres8. The Cats of Cheshire9. Reconstruction10. Planar enumeration11. The chromatic eigenvalues12. In conclusionBibliographyIndex

Editorial Reviews

"In 1935 Bill Tutte went up to Cambridge University to read for the Natural Sciences Tripos, specialising in chemistry. He also had sufficient interest in mathematical problems to join the Trinity Mathematical Society where he met three mathematics students . . . A problem . . . prompted the four to study the dissection of rectangles into squares and this led them into the realms of graph theory, a subject then researched by comparatively few people. . . . Bill Tutte then turned from chemistry to mathematics and went on to become one of the most distinguished persons in graph theory. . . . [T]he present book . . . is not a comprehensive treatise on graph theory but is restricted to those parts of the subject which Tutte himself researched, telling how he was led to his theorems and their proofs. . . . For those of us who find much research-level mathematical literature heavy going, it is good to have this readable account of how some of the ideas developed."—Mathematical Reviews

"Come, sit down with William T. Tutte, a great mathematician and pleasantly quiet man. He tells you of the friends of his youth and of the problems that filled their lives just before and just after World War II. Reading this book, you will see his early interest in the Hamiltonian cycle problem, his development of algebraic techniques in graph theory, the reconstruction conjecture, graphical enumeration and the Tutte polynomial, and much more. You will come to understand a fine man as well as gain insight into extraordinary mathematics. Tutte's book presents the deterministic side of graph theory. It describes the mathematical life journey of one of the world's great mathematicians. To an outsider, the topics he studied may seem unconnected. This book reveals their close connections, however, and they are deep and extensive. It also shows the very great attention to details that is visible in all of Tutte's work." — Arthur M. Hobbs, American Mathematical Monthly, April 2001

From the Publisher