The Foundations of Topological Graph Theory - Hardcover

Bonnington, C.P.; Little, C.H.C.

Hardcover

ISBN 10: 0387945571 ISBN 13: 9780387945576

Publisher: Springer-Verlag New York Inc., 1995

Synopsis

This is a text on topological graph theory written from a purely combinatorial viewpoint. The aim is to develop a rigorous approach to the foundation of the subject, and the book should therefore appeal to graduate students and researchers in topological graph theory. The basic tool used is the idea of a 3-graph which is a cubic graph endowed with a proper edge colouring in three colours. A special case of a 3-graph, called a gem, provides a model for a cellular imbedding of a graph in a surface. Thus theorems about imbeddings of graphs become theorems about gems. The book shows many of these theorems generalize to theorems about 3-graphs.

About this title

From the Back Cover

This book on topological graph theory is written from a purely combinatorial viewpoint. Its aim is to develop a rigorous approach to the foundations of the subject. The book should therefore appeal to graduate students and researchers in topological graph theory. The basic tool used is the idea of a 3-graph, which is a cubic graph endowed with a proper edge coloring in three colors. A special case of a 3-graph, called a gem, provides a model for a cellular embedding of a graph in a surface. Thus, theorems about embeddings of graphs become theorems about gems. The authors show that many of these theorems generalize to theorems about 3-graphs. Thus, results such as the classification of surfaces, and the theorem that the first Betti number of a surface is the largest number of closed curves that can be drawn on the surface without dividing it into two or more regions, find a general setting in the theory of 3-graphs. The book therefore uses 3-graphs to develop the foundations of topological graph theory and differs in this way from other books on this subject. Readers should find in its pages a fresh approach to a subject with which they may already have some familiarity.

Edition details

• Publisher: Springer-Verlag New York Inc.
• Publication date: 1995
• Language: English
• ISBN 10: 0387945571
• ISBN 13: 9780387945576
• Binding: Hardcover
• Number of pages: 177