Bollobas B. Modern Graph Theory 2008

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Bollobas B. Modern Graph Theory 2008

Textbook in PDF and DJVU formats Apologia Preface Fundamentals Definitions Paths, Cycles, and Trees Hamilton Cycles and Euler Circuits Planar Graphs An Application of Euler Trails to Algebra Exercises Notes Electrical Networks Graphs and Electrical Networks Squaring the Square Vector Spaces and Matrices Associated with Graphs Exercises Notes Flows, Connectivity and Matching Flows in Directed Graphs Connectivity and Menger's Theorem Matching Tutte's 1-Factor Theorem Stable Matchings Exercises Notes Extremal Problems Paths and Cycles Complete Subgraphs Hamilton Paths and Cycles The Structure of Graphs Szemerédi's Regularity Lemma Simple Applications of Szemerédi's Lemma Exercises Notes Colouring Vertex Colouring Edge Colouring Graphs on Surfaces List Colouring Perfect Graphs Exercises Notes Ramsey Theory The Fundamental Ramsey Theorems Canonical Ramsey Theorems Ramsey Theory For Graphs Ramsey Theory for Integers Subsequences Exercises Notes Random Graphs The Basic Models—The Use of the Expectation Simple Properties of Almost All Graphs Almost Determined Variables—The Use of the Variance Hamilton Cycles—The Use of Graph Theoretic Tools The Phase Transition Exercises Notes Graphs, Groups and Matrices Cayley and Schreier Diagrams The Adjacency Matrix and the Laplacian Strongly Regular Graphs Enumeration and Pólya's Theorem Exercises Notes Random Walks on Graphs Electrical Networks Revisited Electrical Networks and Random Walks Hitting Times and Commute Times Conductance and Rapid Mixing Exercises Notes The Tutte Polynomial Basic Properties of the Tutte Polynomial The Universal Form of the Tutte Polynomial The Tutte Polynomial in Statistical Mechanics Special Values of the Tutte Polynomial A Spanning Tree Expansion of the Tutte Polynomial Polynomials of Knots and Links Exercises Notes Symbol Index Name Index Subject Index