The Foundations of Topological Graph Theory - Tapa dura

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

 
9780387945576: The Foundations of Topological Graph Theory
Tapa dura
ISBN 10: 0387945571 ISBN 13: 9780387945576
Editorial: Springer-Verlag New York Inc., 1995

Sinopsis

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.

"Sinopsis" puede pertenecer a otra edición de este libro.

Reseña del editor

This is not a traditional work on topological graph theory. No current graph or voltage graph adorns its pages. Its readers will not compute the genus (orientable or non-orientable) of a single non-planar graph. Their muscles will not flex under the strain of lifting walks from base graphs to derived graphs. What is it, then? It is an attempt to place topological graph theory on a purely combinatorial yet rigorous footing. The vehicle chosen for this purpose is the con­ cept of a 3-graph, which is a combinatorial generalisation of an imbedding. These properly edge-coloured cubic graphs are used to classify surfaces, to generalise the Jordan curve theorem, and to prove Mac Lane's characterisation of planar graphs. Thus they playa central role in this book, but it is not being suggested that they are necessarily the most effective tool in areas of topological graph theory not dealt with in this volume. Fruitful though 3-graphs have been for our investigations, other jewels must be examined with a different lens. The sole requirement for understanding the logical development in this book is some elementary knowledge of vector spaces over the field Z2 of residue classes modulo 2. Groups are occasionally mentioned, but no expertise in group theory is required. The treatment will be appreciated best, however, by readers acquainted with topology. A modicum of topology is required in order to comprehend much of the motivation we supply for some of the concepts introduced.

Contraportada

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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer-Verlag New York Inc.
Año de publicación
1995
Idioma
Inglés
ISBN 10 
0387945571
ISBN 13 
9780387945576
Encuadernación
Tapa dura
Número de páginas
177
Contacto del fabricante
no disponible
Persona responsable
no disponible

Otras ediciones populares con el mismo título

9781461275732: The Foundations of Topological Graph Theory

Edición Destacada

ISBN 10:  1461275733 ISBN 13:  9781461275732
Editorial: Springer, 2011
Tapa blanda