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INTRODUCTION TO GRAPH THEORY
INTRODUCTION TO GRAPH THEORY
Richard J. Trudeau
DOVER PUBLICATIONS, INC.
New York
Copyright
Copyright © 1993 by Richard J. Trudeau.
Copyright © 1976 by the Kent State University Press.All rights reserved.
Bibliographical Note
This Dover edition, first published in 1993, is a slightly corrected, enlarged republication of the work first published by The Kent State University Press, Kent, Ohio, 1976. For this edition the author has added a new section, “Solutions to Selected Exercises,” and corrected a few typographical and graphical errors.
Library of Congress Cataloging-in-Publication Data
Trudeau, Richard J.
Introduction to graph theory / Richard J. Trudeau.
p. cm.
Rev. ed. of: Dots and lines, 1976.
Includes bibliographical references and index.
ISBN-13: 978-0-486-67870-2
ISBN-10: 0-486-67870-9
1. Graph theory. I. Trudeau, Richard J. Dots and lines. II. Title.
QA166.T74 1993
511'.5—dc20
93-32996
CIP
Manufactured in the United States by Courier Corporation67870908www.doverpublications.com
To Dick Barbieri and Chet Raymo
TABLE OF 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, K5, 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- ............

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