| Description |
ix, 178 pages : illustrations ; 24 cm |
| Contents |
1. Introduction -- 2. Maps -- 3. Classification of Surfaces -- 4. Consistent and Coherent Orientations -- 5. Non-separating Curves in Surfaces -- 6. Mac Lane's Theorem for 3-Graphs -- 7. Kuratowski's Theorem -- 8. Duality -- 9. Rings of Bonds -- 10. Bridges |
| Summary |
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 |
|
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 |
| Bibliography |
Includes bibliographical references (pages [161]-163) and index |
| Subject |
Topological graph theory.
|
| Author |
Little, Charles H. C. (Charles Huw Crawford), 1947-
|
| LC no. |
95030507 |
| ISBN |
0387945571 (hardcover : alk. paper) |
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