William Tutte, one of the founders of modern graph theory, provides a unique and personal introduction to the field. Instead of a typical survey, the author looks back at the areas which interested him most, discussing why he pursued certain problems and how he and his colleagues solved them. The book's extensive references make it a useful starting point for research as well as an important document for anyone interested in the history of graph theory. The author begins with the problems he worked on as an undergraduate at Cambridge and goes on to cover subjects such as combinatorial problems in chess, algebra in graph theory, reconstruction of graphs, symmetry in graphs, and the chromatic eigenvalues. In each case he mixes fascinating historical and biographical information with engaging descriptions of important results.
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Editorial Reviews
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"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
About the Author
W. T. Tutte is a Professor, Department of Combinatorics and Optimization at University of Waterloo.
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Most Helpful Customer Reviews
2 of 2 people found the following review helpful:
4.0 out of 5 stars
An introduction to some advanced theorems on graphs,
By Charles Ashbacher (Marion, Iowa United States) - See all my reviews (TOP 500 REVIEWER) (VINE VOICE) (HALL OF FAME REVIEWER)
This review is from: Graph Theory As I Have Known It (Oxford Lecture Series in Mathematics and Its Applications) (Hardcover)
The author has spent most of his professional life pondering some of the more substantial problems in graph theory. This book is not a comprehensive treatise on the subject but an organized collection of a series of lectures that he delivered in 1984. The lectures were just as much an attempt to provide insight into the process that led to some advanced theorems as about the theorems themselves. For this reason, the book is best suited for the beginning graduate student with some experience in the field.Some of the problems covered in the book are: the knight's tour problem as an exercise in graph theory, subgraphs and Hamiltonian circuits; algebra in graph theory, symmetry in graphs and graphs on spheres. Throughout the explanations of the problems and the solution strategies, it is impossible not to appreciate the effort that was put forward to solve them. Tutte is clearly one of the leading authorities in graph theory and good at explaining what graph theory is all about. This is not an easy book to read, yet it is readable. It would be ideal as the material for a graduate seminar in graph theory or a text in advanced topics.
5.0 out of 5 stars
Inside the mind of a great mathematician,
By FELIU D SAGOLS (Vermon, USA) - See all my reviews
This review is from: Graph Theory As I Have Known It (Oxford Lecture Series in Mathematics and Its Applications) (Hardcover)
It is unquestionably that W. T. Tutte is today one the greatest mathematicians in the world. I read this book with great enthusiasm because the author explains, with the work that made his fame, the most difficult part of the discovery of mathematics: The creativity involved.The students will find in this book a great motivation to thinking in mathematics. For the experimented mathematician this book will make clear the born procces of some classic results in graph theory. This is an excellent book, is just the story of a life of work and fun.
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Inside This Book
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First Sentence:
This book is about "Graph Theory as I have known it". Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
constrained chromials, strict triangulations, elementary coboundary, bicubic map, rooted triangulations, standard representative matrix, chromatic sums, squared rectangles, coboundary group, border vertices, triangulated triangle, cubic graph, alternating map, dichromatic polynomial, planar duality, algebraic duality, chromatic polynomials, reconstruction conjecture, constituent triangles, disjoint circuits, binary matroid, cubic maps, colour theorem, peripheral circuits, residual domain Key Phrases - Capitalized Phrases (CAPs): (learn more)
Tait's Conjecture, Four Colour Problem, Kelly's Lemma, Petersen's Theorem, Reconstruction Conjecture, Smith's Theorem, Combinatorial Topology, Four Colour Theorem, Golden Identity, Grinberg's Theorem, Matrix-Tree Theorem, Dick Wick Hall, Hall's Theorem, Jacobi's Theorem, Birkhoff Lewis, Hassler Whitney, Kuratowski's Theorem, Reconstruction Theory, University of Toronto New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This book is about "Graph Theory as I have known it". Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
constrained chromials, strict triangulations, elementary coboundary, bicubic map, rooted triangulations, standard representative matrix, chromatic sums, squared rectangles, coboundary group, border vertices, triangulated triangle, cubic graph, alternating map, dichromatic polynomial, planar duality, algebraic duality, chromatic polynomials, reconstruction conjecture, constituent triangles, disjoint circuits, binary matroid, cubic maps, colour theorem, peripheral circuits, residual domain Key Phrases - Capitalized Phrases (CAPs): (learn more)
Tait's Conjecture, Four Colour Problem, Kelly's Lemma, Petersen's Theorem, Reconstruction Conjecture, Smith's Theorem, Combinatorial Topology, Four Colour Theorem, Golden Identity, Grinberg's Theorem, Matrix-Tree Theorem, Dick Wick Hall, Hall's Theorem, Jacobi's Theorem, Birkhoff Lewis, Hassler Whitney, Kuratowski's Theorem, Reconstruction Theory, University of Toronto New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 5
books:
- Graph Theory (Cambridge Mathematical Library) by W. T. Tutte on 7 pages
- English Authors Series: Lewis Carroll, Revised Edition (Twayne's English Authors Series) by Richard Michael Kelly on page 110
- Scientific American Book of Mathematical Puzzles and Diversions by Martin Gardner in Back Matter
- America in the Time of George Washington: The Story of Our Nation from Coast to Coast, from 1747 to 1803 by Sally Senzell Isaacs in Back Matter
- Mathematical Puzzles of Sam Loyd by Sam Loyd in Back Matter
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