現代グラフ理論 Modern Graph Theory (Graduate Texts in Mathematics Vol.184) （1998. XIII, 394 p. w. 118 figs. 24,5 cm）

Bollobas, Bela

SPRINGER, BERLIN（1998発売）

• 製本 Hardcover:ハードカバー版／ページ数 394 p.
• 商品コード 9780387984919

基本説明

Contents: Fundamentals; Electrical Networks; Flows, Connectivity and Matching; Extremal Problems; Colouring; Ramsey Theory; Random Graphs; Graphs, Groups and Matrices; Random Walks on Graphs; The Tutte Polynomial.

Full Description

This text is an in-depth account of graph theory. It reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains descriptive passages designed to convey the flavour of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as colouring, matching, extremal theory, and algebraic graph theory, the book presents an account of newer topics, including: Szemer'edi's Regularity Lemma and its use; Shelah's extension of the Hales-Jewett Theorem; the precise nature of the phase transition in a random graph process; the connection between electrical networks and random walks on graphs; and the Tutte polynomial and its cousins in knot theory.