Cycles and Bridges in Graphs

Voß, Heinz-Jürgen:

ISBN 10: 3326003684 / ISBN 13: 9783326003689

Published by Berlin : Deutscher Verlag der Wissenschaften, 1991

About this Item

XII, 271 Pages ; With 81 Figures Original Hardcover (Pappband) mit Bibliotheksschild auf Vorderdeckel. Innen mit Bibliotheksstempeln, sehr sauberes Exemplar. Englische Sprache. - Original Hardboard with Library label on front cover. Inside with Library stamps, in very good condition. English Language B15-03-02D|S99 Altersfreigabe FSK ab 0 Jahre Sprache: Englisch Gewicht in Gramm: 520.

Seller Inventory # 62826

Bibliographic Details

• Title: Cycles and Bridges in Graphs
• Publisher: Berlin : Deutscher Verlag der Wissenschaften
• Publication Date: 1991
• Language: English
• ISBN 10: 3326003684
• ISBN 13: 9783326003689
• Binding: 24,5 x 16,5 cm
• Edition: Mathematische Monographien ; Band 23.
• Condition: Gut
• Weight: 520 grams
• Seller catalogs:
  • Modernes Antiquariat

About this title

Synopsis

Since the first book on graph theory by D.Kőnig appeared in 1936, this branch of mathematics has enormously developed. This is true for both the theory and the applications to many problems of practical interest. The study of properties of bridges of certain subgraphs yields interesting results in various fields, especially in constructing graph theoretical algorithms. The book is devoted to cycles and bridges in (finite, undirected, simple) graphs, particularly to bridges of cycles. The emphasis of the book is on the concept of bridge. This concept was first introduced by Tutte and Ore and and is now widely used in graph theory. In chapter 1 overlap graphs (bridge graphs) are introduced and their applications to planar & non-planar graphs are treated (Kuratowski's theorem, Hamiltonian cycles in planar graphs etc). Graphs whose cycles (or paths) have only one bridge are investigated in chapter 2. Chapter 3 is concerned with intersection patterns of longest cycles. Upper bounds for the circumference of bridges of longest cycles are determined. Ch. 4-6 are devoted to graphs with high symmetries, i.e., with many isomorphic bridges. The obtained results are applied to critical graphs. The Reconstruction problem is solved for some classes of such highly symmetric graphs. Chapters 7-11 are concerned with valency conditions and conditions on the number of edges for the existence of long cycles through given vertices and edges and for the existence of cycles with many diagonals. In chapters 9-10 the girth of the graphs is involved. All cubic graphs with given circumference having maximum order are determined in chapter 11. This monograph finishes with a large bibliography which gives a survey on publications to this topic up to now. The level of development of the theory is the reason enough for writing this monograph which shows once more that graph theory is undoubtedly one of the simplest and most elegant mathematical subjects possessing a wide variety of applications.