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9780486678702

Introduction to Graph Theory

by
  • ISBN13:

    9780486678702

  • ISBN10:

    0486678709

  • Format: Paperback
  • Copyright: 1994-02-09
  • Publisher: Dover Publications

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Summary

A stimulating excursion into pure mathematics aimed at "the mathematically traumatized," but great fun for mathematical hobbyists and serious mathematicians as well. This book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. Includes exercises. 1976 edition.

Table of Contents

Preface
Pure Mathematics
Introduction
Euclidean Geometry as Pure Mathematics
Games
Why Study Pure Mathematics?
What's Coming
Suggested Reading
Graphs
Introduction
Sets
Paradox
Graphs
Graph diagrams
Cautions
Common Graphs
Discovery
Complements and Subgraphs
Isomorphism
Recognizing Isomorphic Graphs
Semantics
The Number of Graphs Having a Given nu
Exercises
Suggested Reading
Planar Graphs
Introduction
UG, K subscript 5, and the Jordan Curve Theorem
Are there More Nonplanar Graphs?
Expansions
Kuratowski's Theorem
Determining Whether a Graph is Planar or Nonplanar
Exercises
Suggested Reading
Euler's Formula
Introduction
Mathematical Induction
Proof of Euler's Formula
Some Consequences of Euler's Formula
Algebraic Topology
Exercises
Suggested Reading
Platonic Graphs
Introduction
Proof of the Theorem
History
Exercises
Suggested Reading
Coloring
Chromatic Number
Coloring Planar Graphs
Proof of the Five Color Theorem
Coloring Maps
Exercises
Suggested Reading
The Genus of a Graph
Introduction
The Genus of a Graph
Euler's Second Formula
Some Consequences
Estimating the Genus of a Connected Graph; g-Platonic Graphs
The Heawood Coloring Theorem
Exercises
Suggested Reading
Euler Walks and Hamilton Walks
Introduction
Euler Walks
Hamilton Walks
Multigraphs
The Konigsberg Bridge Problem
Exercises
Suggested Reading
Afterword
Solutions to Selected Exercises
Index
Special symbols
Table of Contents provided by Publisher. All Rights Reserved.

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