Extremal Graph Theory,9780486435961

Extremal Graph Theory

by
ISBN13: 9780486435961
ISBN10: 0486435962
Format: Paperback
Pub. Date: 2004-06-04
Publisher(s): Dover Publications
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Summary

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. 1978 edtion.

Table of Contents

Preface vii
Basic Definitions xiii
Connectivity
1(49)
Elementary Properties
2(5)
Menger's Theorem and its Consequences
7(4)
The Structure of 2- and 3-Connected Graphs
11(6)
Minimally k-Connected Graphs
17(12)
Graphs with Given Maximal Local Connectivity
29(16)
Exercises, Problems and Conjectures
45(5)
Matching
50(52)
Fundamental Matching Theorems
52(7)
The Number of 1-Factors
59(8)
f-Factors
67(12)
Matching in Graphs with Restrictions on the Degrees
79(11)
Coverings
90(5)
Exercises, Problems and Conjectures
95(7)
Cycles
102(67)
Graphs with Large Minimal Degree and Large Girth
103(7)
Vertex Disjoint Cycles
110(9)
Edge Disjoint Cycles
119(12)
The Circumference
131(16)
Graphs with Cycles of Given Lengths
147(14)
Exercises, Problems and Conjectures
161(8)
The Diameter
169(49)
Diameter, Maximal Degree and Size
170(11)
Diameter and Connectivity
181(13)
Graphs with Large Subgraphs of Small Diameter
194(12)
Factors of Small Diameter
206(7)
Exercises, Problems and Conjectures
213(5)
Colourings
218(74)
General Colouring Theorems
221(13)
Critical k-Chromatic Graphs
234(9)
Colouring Graphs on Surfaces
243(11)
Sparse Graphs of Large Chromatic Number
254(9)
Perfect Graphs
263(7)
Ramsey Type Theorems
270(10)
Exercises, Problems and Conjectures
280(12)
Complete Subgraphs
292(76)
The Number of Complete Subgraphs
293(16)
Complete Subgraphs of r-Partite Graphs
309(18)
The Structure of Graphs
327(12)
The Structure of Extremal Graphs without Forbidden Subgraphs
339(12)
Independent Complete Subgraphs
351(8)
Exercises, Problems and Conjectures
359(9)
Topological Subgraphs
368(33)
Contractions
369(9)
Topological Complete Subgraphs
378(8)
Semi-Topological Subgraphs
386(11)
Exercises, Problems and Conjectures
397(4)
Complexity and Packing
401(37)
The Complexity of Graph Properties
402(9)
Monotone Properties
411(7)
The Main Packing Theorem
418(7)
Packing Graphs of Small Size
425(4)
Applications of Packing Results to Complexity
429(5)
Exercises, Problems and Conjectures
434(4)
References 438(43)
Index of Symbols 481(4)
Index of Definitions 485

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