目錄
Apologia
Preface
Ⅰ Fundamentals
Ⅰ.1 Definitions
Ⅰ.2 Paths, Cycles, and Trees
Ⅰ.3 Hamilton Cycles and Euler Circuits
Ⅰ.4 Planar Graphs
Ⅰ.5 An Application of Euler Trails to Algebra
Ⅰ.6 Exercises
Ⅱ Electrical Networks
Ⅱ.1 Graphs and Electrical Networks
Ⅱ.2 Squaring the Square
Ⅱ.3 Vector Spaces and Matrices Associated with Graphs
Ⅱ.4 Exercises
Ⅱ.5 Notes
Ⅲ Flows, ConnectⅣity and Matching
Ⅲ.1 Flows in Directed Graphs
Ⅲ.2 ConnectⅣity and Menger's Theorem
Ⅲ.3 Matching
Ⅲ.4 Tutte's 1-Factor Theorem
Ⅲ.5 Stable Matchings
Ⅲ.6 Exercises
Ⅲ.7 Notes
Ⅳ Extremal Problems
Ⅳ.1 Paths and Cycles
Ⅳ.2 Complete Subgraphs
Ⅳ.3 Hamilton Paths and Cycles
Ⅳ.4 The Structure of Graphs
Ⅳ.5 Szemeredi's Regularity Lemma
Ⅳ.6 Simple Applications of Szemer&ti's Lernma
Ⅳ.7 Exercises
Ⅳ.8 Notes
Ⅴ Colouring
Ⅴ.1 Vertex Colouring
Ⅴ.2 Edge Colouring
Ⅴ.3 Graphs on Surfaces
Ⅴ.4 List Colouring
Ⅴ.5 Perfect Graphs
Ⅴ.6 Exercises
Ⅴ.7 Notes
Ⅵ Ramsey Theory
Ⅵ.1 The Fundamental Rarnsey Theorems
Ⅵ.2 Canonical Ramsey Theorems
Ⅵ.3 Ramsey Theory For Graphs
Ⅵ.4 Ramsey Theory for Integers
Ⅵ.5 Subsequances
Ⅵ.6 Exercises
Ⅵ.7 Notes
Ⅶ Random Graphs
Ⅶ.1 The Basic Models---The Use of the Expectation
Ⅶ.2 Simple Properties of Almost All Graphs
Ⅶ.3 Almost Determined VariableskThe Use of the Variance
Ⅶ.4 Hamilton Cycles---The Use of Graph Theoretic Tools.
Ⅶ.5 The Phase Transition
Ⅶ.6 Exercises
Ⅶ.7 Notes
Ⅷ Graphs, Groups and Matrices
Ⅷ.1 Cayley and Schreier Diagrams
Ⅷ.2 The Adjacency Matrix and the Laplacian
Ⅷ.3 Strongly Regular Graphs
Ⅷ.4 Enumeration and P61ya's Theorem
Ⅷ.5 Exercises
Ⅸ Random Walks on Graphs
Ⅸ.1 Electrical Networks Revisited
Ⅸ.2 Electrical Networks and Random Walks
Ⅸ.3 Hitting Times and Commute Times
Ⅸ.4 Conductance and Rapid Mixing
Ⅸ.5 Exercises
Ⅸ.6 Notes
Ⅹ The TaRe Polynomial
Ⅹ.1 Basic Properties of the Tutte Polynomial
Ⅹ.2 The UnⅣersal Form of the Tutte Polynomial
Ⅹ.3 The Tutte Polynomial in Statistical Mechanics
Ⅹ.4 Special Values of the "luRe Polynomial
Ⅹ.5 A Spanning Tree Expansion of the Tutte Polynomial
Ⅹ.6 Polynomials of Knots and Links
Ⅹ.7 Exercises
Ⅹ.8 Notes
Symbol Index
Name Index
Subject Index
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