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OverviewFull Product DetailsAuthor: Bela BollobasPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: 1st ed. 1998. Corr. 2nd printing 2002 Volume: 184 Dimensions: Width: 15.50cm , Height: 2.10cm , Length: 23.50cm Weight: 1.270kg ISBN: 9780387984889ISBN 10: 0387984887 Pages: 394 Publication Date: 01 July 1998 Audience: College/higher education , Undergraduate , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsI 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.- W.4 The Structure of Graphs.- IV 5 Szemerédi’s Regularity Lemma.- IV 6 Simple Applications of Szemerédi’s Lemma.- 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 Ramsey Theorems.- VI.2 Canonical Ramsey Theorems.- VI.3 Ramsey Theory For Graphs.- VI.4 Ramsey Theory for Integers.- VI.5 Subsequences.- 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 Variables-The 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 Pólya’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 Tutte Polynomial.- X.1 Basic Properties of the Tutte Polynomial.- X.2The Universal Form of the Tutte Polynomial.- X.3 The Tutte Polynomial in Statistical Mechanics.- X.4 Special Values of the Tutte 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.Reviews<p>., . This book is likely to become a classic, and it deserves to be on the shelf of everyone working in graph theory or even remotely related areas, from graduate student to active researcher. --MATHEMATICAL REVIEWS Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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