A Textbook of Graph Theory

Graph theory has experienced a tremendous growth during the 20th century. One of the main reasons for this phenomenon is the applicability of graph theory in other disciplines such as physics, chemistry, psychology, sociology, and theoretical computer science.

This book aims to provide a solid background in the basic topics of graph theory. It covers Dirac's theorem on k-connected graphs, Harary-Nashwilliam's theorem on the hamiltonicity of line graphs, Toida-McKee's characterization of Eulerian graphs, the Tutte matrix of a graph, Fournier's proof of Kuratowski's theorem on planar graphs, the proof of the nonhamiltonicity of the Tutte graph on 46 vertices and a concrete application of triangulated graphs. The book does not presuppose deep knowledge of any branch of mathematics, but requires only the basics of mathematics. It can be used in an advanced undergraduate course or a beginning graduate course in graph theory.

Contents

Preface

I Basic Results 1
II Directed Graphs 33
III Connectivity 44
IV Trees 67
V Independent Sets and Matchings 83
VI Eulerian and Hamiltonian Graphs 102
VII Graph Colorings 128
VIII Planarity 152
IX Triangulated Graphs 185
X Applications 199

List of Symbols 213
References 217
Index