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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Intended for a broad range of readers, including undergraduate students and researchers. Can be read by a mathematician not yet familiar with graph theory, but will also be of interest to researchers since it contains many recent results and partial solutions to some unsolved problems. -- American Mathematical Monthly
The style is clear and lively throughout, and the book contains many exercises and a lengthy bibliography. -- R.J. Wilson, Mathematical Reviews
This monograph should appeal to both researchers and students. It contains enough material for an undergraduate or graduate graph theory course which emphasizes eulerian graphs. But it is also of interest to researchers because it contains many recent results. -- L'Enseignement Mathematique
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