Eulerian graphs and related topics

Herbert Fleischner (Eds.)978-0-444-88395-7, 0444883959, 0444891102

The two volumes comprising Part 1 of this work embrace the theme of Eulerian trails and covering walks. They should appeal both to researchers and students, as they contain enough material for an undergraduate or graduate graph theory course which emphasizes Eulerian graphs, and thus can be read by any mathematician not yet familiar with graph theory. But they are also of interest to researchers in graph theory because they contain many recent results, some of which are only partial solutions to more general problems. A number of conjectures have been included as well. Various problems (such as finding Eulerian trails, cycle decompositions, postman tours and walks through labyrinths) are also addressed algorithmically.

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Table of contents :
Content:
General Editor
Page ii

Edited by
Page iii

Copyright page
Page iv

Dedication
Page v

Portrait of Leonard Euler (1707-1783) by the Alsatian painter Franz Bernhard Frey (1716-1806).
Page vi

Preface
Pages vii-ix

Chapter I Introduction
Pages I.1-I.5

Chapter II Three Pillars of Eulerian Graph Theory
Pages II.1-II.26

Chapter III Basic Concepts and Preliminary Results
Pages III.1-III.76

Chapter IV Characterization Theorems and Corollaries
Pages IV.1-IV.20

Chapter V Euler Revisited and an Outlook on Some Generalizations
Pages V.1-V.8

Chapter VI Various Types of Eulerian Trails
Pages VI.1-VI.173

Chapter VII Transformations of Eulerian Trails
Pages VII.1-VII.55

Bibliography Review Article
Pages A.1-A.15

Index
Pages B.1-B.9