# Book:Richard J. Trudeau/Dots and Lines

## Richard J. Trudeau: Introduction to Graph Theory

Published $\text {1976}$, Kent State University Press.

### Contents

Preface
1. PURE MATHEMATICS
Introduction ... Euclidean Geometry as Pure Mathematics ... Games ... Why Study Pure Mathematics? ... What's Coming ... Suggested Reading
2. 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 $v$ ... Exercises ... Suggested Reading
3. PLANAR GRAPHS
Introduction ... $UG$, $K_5$, 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
4. EULER'S FORMULA
Introduction ... Mathematical Induction ... Proof of Euler's Formula ... Some Consequences of Euler's Formula ... Algebraic Topology ... Exercises ... Suggested Reading
5. PLATONIC GRAPHS
Introduction ... Proof of the Theorem ... History ... Exercises ... Suggested Reading
6. COLORING
Chromatic Number ... Coloring Planar Graphs ... Proof of the Five Color Theorem ... Coloring Maps ... Exercises ... Suggested Reading
7. 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
8. EULER WALKS AND HAMILTONIAN WALKS
Introduction ... Euler Walks ... Hamilton Walks ... Multigraphs ... The Königsberg Bridge Problem ... Exercises ... Suggested Reading
Afterword
Index
Special symbols

## Further Editions

1993: Richard J. Trudeau: Introduction to Graph Theory