Graphs on Surfaces by Carsten Thomassen

Graphs on Surfaces by Carsten Thomassen

Graph theory is one of the fastest growing branches of mathematics. Until recently, it was regarded as a branch of combinatorics and was best known by the famous four-color theorem stating that any map can be colored using only four colors such that no two bordering countries have the same color. Now graph theory is an area of its own with many deep results and beautiful open problems. Graph theory has numerous applications in almost every field of science and has attracted new interest because of its relevance to such technological problems as computer and telephone networking and, of course, the internet. In this new book in the Johns Hopkins Studies in the Mathematical Science series, Bojan Mohar and Carsten Thomassen look at a relatively new area of graph theory: that associated with curved surfaces. Graphs on surfaces form a natural link between discrete and continuous mathematics. The book provides a rigorous and concise introduction to graphs on surfaces and surveys some of the recent developments in this area. Among the basic results discussed are Kuratowski's theorem and other planarity criteria, the Jordan Curve Theorem and some of its extensions, the classification of surfaces, and the Heffter-Edmonds-Ringel rotation principle, which makes it possible to treat graphs on surfaces in a purely combinatorial way. The genus of a graph, contractability of cycles, edge-width, and face-width are treated purely combinatorially, and several results related to these concepts are included. The extension by Robertson and Seymour of Kuratowski's theorem to higher surfaces is discussed in detail, and a shorter proof is presented. The book concludes with a survey of recent developments on coloring graphs on surfaces.

As major players in an active field, the authors never make a wrong move: they choose the right topics, treat them to the right depth, rethink the classical arguments when appropriate, and anticipate the reader's questionsAny undergraduate who penetrates even two or three chapters will learn a great deal of important mathematics, and rather painlessly at that. Surely a classic. Choice

Bojan Mohar is a professor in the Department of Mathematics at the University of Ljubljana in Slovenia and a member of the Engineering Academy of Slovenia. Carsten Thomassen is a professor at the Mathematical Institute of the Technical University of Denmark, the editor-in-chief of the Journal of Graph Theory, and a member of the Royal Danish Academy of Sciences and Letters.

SKU	Nicht verfügbar
ISBN 13	9780801866890
ISBN 10	0801866898
Titel	Graphs on Surfaces
Autor	Carsten Thomassen
Serie	Johns Hopkins Studies In The Mathematical Sciences
Buchzustand	Nicht verfügbar
Bindungsart	Hardback
Verlag	Johns Hopkins University Press
Erscheinungsjahr	2001-09-27
Seitenanzahl	304
Hinweis auf dem Einband	Die Abbildung des Buches dient nur Illustrationszwecken, die tatsächliche Bindung, das Cover und die Auflage können sich davon unterscheiden.
Hinweis	Nicht verfügbar