# A Textbook of Graph Theory

Part of the Universitext book series (UTX)

Part of the Universitext book series (UTX)

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.

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- DOI https://doi.org/10.1007/978-1-4419-8505-7
- Copyright Information Springer-Verlag New York, Inc. 2000
- Publisher Name Springer, New York, NY
- eBook Packages Springer Book Archive
- Print ISBN 978-1-4612-6422-4
- Online ISBN 978-1-4419-8505-7
- Series Print ISSN 0172-5939
- Series Online ISSN 2191-6675
- About this book