Eulerian Graphs and Related Topics: Part 1, Volume 1

Description

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. 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