Can be used as a college level text for mathematics, computer science, or engineering students. Also suitable for a general education course at a liberal arts college, or for self-study.

*Graph Theory* presents a natural, reader-friendly way to learn some of the essential ideas of graph theory starting from first principles. The book combines the features of a textbook with those of a problem workbook. The material is presented through a series of approximately 360 strategically placed problems with connecting text. This is supplemented by 280 additional problems that are intended to be used as homework assignments. Concepts of graph theory are introduced, developed, and reinforced by working through leading questions posed in the problems.

### Table of Contents

Preface

Introduction: Problems of Graph Theory

Basic Concepts

Isomorphic Graphs

Bipartite Graphs

Trees and Forests

Spanning Tree Algorithms

Euler Paths

Hamilton Paths and Cycles

Planar Graphs

Independence and Covering

Connections and Obstructions

Vertex Coloring

Edge Coloring

Matching Theory for Bipartite Graphs

Applications of Matching Theory

Cycle-Free Digraphs

Network Flow Theory

Flow Problems with Lower Bounds

Answers to Selected Problems

Index

About the Author

### About the Author

**Daniel A. Marcus** received his PhD from Harvard University. He was a J. Willard Gibbs Instructor at Yale University from 1972-74 and Professor of Mathematics at California State Polytechnic University, Pomona from 1979-2004. Marcus has published research papers in the areas of graph theory, number theory, and combinatorics. He is the author of the following books: *Combinatorics: A Problem Oriented Approach* (also with the MAA), *Differential Equations: An Introduction*, and *Number Fields*.