グラフ理論(第4版)<br>Graph Theory (Graduate Texts in Mathematics) 〈Vol. 173〉 (4TH)

グラフ理論(第4版)
Graph Theory (Graduate Texts in Mathematics) 〈Vol. 173〉 (4TH)

  • ただいまウェブストアではご注文を受け付けておりません。 ⇒古書を探す
  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 410 p.
  • 言語 ENG
  • 商品コード 9783642142789

基本説明

現代グラフ理論の定番テキスト、4年振りの改訂版。
This standard textbook of modern graph theory, now in its fourth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study.

Full Description


Almosttwodecadeshavepassedsincetheappearanceofthosegrapht- ory texts that still set the agenda for most introductory courses taught today. The canon created by those books has helped to identify some main?eldsofstudyandresearch,andwilldoubtlesscontinuetoin?uence the development of the discipline for some time to come. Yet much has happened in those 20 years, in graph theory no less thanelsewhere: deepnewtheoremshavebeenfound,seeminglydisparate methods and results have become interrelated, entire new branches have arisen. To name just a few such developments, one may think of how the new notion of list colouring has bridged the gulf between inva- ants such as average degree and chromatic number, how probabilistic methods andtheregularity lemmahave pervadedextremalgraphtheory and Ramsey theory, or how the entirely new ?eld of graph minors and tree-decompositions has brought standard methods of surface topology to bear on long-standing algorithmic graph problems. Clearly, then, the time has come for a reappraisal: what are, today, the essential areas, methods and results that should form the centre of an introductory graph theory course aiming to equip its audience for the most likely developments ahead? I have tried in this book to o?er material for such a course. In view of the increasing complexity and maturity of the subject, I have broken with the tradition of attempting to cover both theory and app- cations: this book o?ers an introduction to the theory of graphs as part of (pure) mathematics; it contains neither explicit algorithms nor `real world' applications.

Contents

The Basics.- Matching Covering and Packing.- Connectivity.- Planar Graphs.- Colouring.- Flows.- Extremal Graph Theory.- Infinite Graphs.- Ramsey Theory for Graphs.- Hamilton Cycles.- Random Graphs.- Minors Trees and WQO.