Extremal Graph Theory

ISBN-10: 0486435962

ISBN-13: 9780486435961

Edition: 2004

Authors: Bela Bollobas

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Description:

The ever-expanding field of extremal graph theory encompasses an array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume presents a concise yet comprehensive treatment, featuring complete proofs for almost all of its results and numerous exercises. Although geared toward mathematicians and research students, much of Extremal Graph Theory is accessible even to undergraduate students of mathematics. Pure mathematicians will find it a valuable resource in terms of its unusually large collection of results and concise proofs, and professionals in other fields with an interest in the applications of graph theory will also appreciate its precision and scope. 1978 ed.
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Book details

List price: $29.95
Copyright year: 2004
Publisher: Dover Publications, Incorporated
Publication date: 6/4/2004
Binding: Paperback
Pages: 512
Size: 5.25" wide x 8.25" long x 1.00" tall
Weight: 1.188
Language: English

Preface
Basic Definitions
Connectivity
Elementary Properties
Menger's Theorem and its Consequences
The Structure of 2- and 3-Connected Graphs
Minimally k-Connected Graphs
Graphs with Given Maximal Local Connectivity
Exercises, Problems and Conjectures
Matching
Fundamental Matching Theorems
The Number of 1-Factors
f-Factors
Matching in Graphs with Restrictions on the Degrees
Coverings
Exercises, Problems and Conjectures
Cycles
Graphs with Large Minimal Degree and Large Girth
Vertex Disjoint Cycles
Edge Disjoint Cycles
The Circumference
Graphs with Cycles of Given Lengths
Exercises, Problems and Conjectures
The Diameter
Diameter, Maximal Degree and Size
Diameter and Connectivity
Graphs with Large Subgraphs of Small Diameter
Factors of Small Diameter
Exercises, Problems and Conjectures
Colourings
General Colouring Theorems
Critical k-Chromatic Graphs
Colouring Graphs on Surfaces
Sparse Graphs of Large Chromatic Number
Perfect Graphs
Ramsey Type Theorems
Exercises, Problems and Conjectures
Complete Subgraphs
The Number of Complete Subgraphs
Complete Subgraphs of r-Partite Graphs
The Structure of Graphs
The Structure of Extremal Graphs without Forbidden Subgraphs
Independent Complete Subgraphs
Exercises, Problems and Conjectures
Topological Subgraphs
Contractions
Topological Complete Subgraphs
Semi-Topological Subgraphs
Exercises, Problems and Conjectures
Complexity and Packing
The Complexity of Graph Properties
Monotone Properties
The Main Packing Theorem
Packing Graphs of Small Size
Applications of Packing Results to Complexity
Exercises, Problems and Conjectures
References
Index of Symbols
Index of Definitions
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