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本书并不是一本论文集，而是一系列讲稿的有机组合。本书涉及了Menger定理、重构、矩阵—树定理、Brooks定理、Grinberg定理、平面图等核心论题。在讲述时不仅关注原理本身，而且关注其推导过程。如果想对图论有个基本的了解，本书是最佳选择。另外，书中每一章都附有习题、注记和详尽的参考文献。

“相信本书会对在坚实的理论与技术基础上搭建起图论的大厦起到十分重要的作用。”

——Crispin St.J.A. Nash-Williams教授，里丁大学

W．T．Tutte已故著名数学家，现代图论奠基人之一。他于1948年获得剑桥大学博士学位；1942年至1949年担任三一学院评论员；1948年至1962年执教于多伦多大学。他是加拿大皇家科学院院士，曾被授予HenryMarshallTory奖。1982年，加拿大议会授予他IzaakWaltonKillam纪念奖。除本书外，他还著有拟阵论方面的书籍。他生前还多年担任《Journal of Combinatorial Theory》杂志主编。

Editor's Statement
Foreword
Introduction
Chapter I Graphs and Subgraphs
I.1 Definitions
1.2 Isomorphism
1.3 Subgraphs
1.4 Vertices of attachment
1.5 Components and connection
1.6 Deletion of an edge
1.7 Lists of nonisomorphic connected graphs
1.8 Bridges
1.9 Notes
Exercises
References
Chapter II Contractions and the Theorem of Menger
II.1 Contractions
II.2 Contraction of an edge
II.3 Vertices of attachment
II.4 Separation numbers
II.5 Menger's Theorem
II.6 Hall's Theorem
II.7 Notes
Exercises
References
Chapter III 2-Connection
III.1 Separable and 2-connected graphs
III.2 Constructions for 2-connected graphs
III.3 Blocks
III.4 Arms
III.5 Deletion and contraction of an edge
II1.6 Notes
Exercises
References
Chapter IV 3-Connection
IV.1 Multiple connection
IV.2 Some constructions for 3-connected graphs
IV.3 3-blocks
IV.4 Cleavages
IV.5 Deletions and contractions of edges
IV.6 The Wheel Theorem
IV.7 Notes
Exercises
References
Chapter V Reconstruction
V.I The Reconstruction Problem
V.2 Theory and practice
V.3 Kelly's Lemma
V.4 Edge-reconstruction
V.5 Notes
Exercises
References
Chapter VI Digraphs and Paths
VI.1 Digraphs
VI.2 Paths
VI.3 The BEST Theorem
VI.4 The Matrix-Tree Theorem
VI.5 The Laws of Kirchhoff
VI.6 Identification of vertices
VI.7 Transportation Theory
VI.8 Notes
Exercises
References
Chapter VII Alternating Paths
VII.1 Cursality
VII.2 The bicursal subgraph
VII.3 Bicursal units
VII.4 Alternating barriers
VII.5 f-factors and f-barriers
VII.6 The f-factor theorem
VII.7 Subgraphs of minimum deficiency
VII.8 The bipartite case
VII.9 A theorem of Erdos and Gallai
VII.10 Notes
Exercises
References
Chapter VIII Algebraic Duality
VIII.I Chain-groups
VIII.2 Primitive chains
VIII.3 Regular chain-groups
VIII.4 Cycles
VIII.5 Coboundaries
VIII.6 Reductions and contractions
VIII.7 Algebraic duality
VIII.8 Connectivity
VIII.9 On transportation theory
VIII.10 Incidence matrices
VIII.11 Matroids
VIII.12 Notes
Exercises
References
Chapter IX Polynomials Associated with Graphs
IX.1 V-functions
IX.2 The chromatic polynomial
IX.3 Colorings of graphs
IX.4 The flow polynomial
IX.5 Tait colorings
IX.6 The dichromate of a graph
IX.7 Some remarks on reconstruction
IX.8 Notes
Exercises
References
Chapter X Combinatorial Maps
X.1 Definitions and preliminary theorems
X.2 Orientability
X.3 Duality
X.4 Isomorphism
X.5 Drawings of maps
X.6 Angles
X.7 Operations on maps
X.8 Combinatorial surfaces
X.9 Cycles and coboundaries
X. 10 Notes
Exercises
References
Chapter XI Planarity
XI.1 Planar graphs
XI.2 Spanning subgraphs
XI.3 Jordan's Theorem
XI.4 Connectivity in planar maps
XI.5 The cross-cut Theorem
XI.6 Bridges
XI.7 An algorithm for planarity
XI.8 Peripheral circuits in 3-connected graphs
XI.9 Kuratowski's Theorem
XI.10 Notes
Exercises
References
Index
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