Eulerian graphs and related topics. Part 1, Volume 1. (English) Zbl 0792.05091

Fleischner, Herbert

Annals of Discrete Mathematics. 45. Amsterdam etc.: North-Holland. xiii, 402 p. (1990).

This welcome book presents the theory of Euclidean graphs and digraphs in a form suitable for students and researchers in graph theory. The author starts by presenting “Three pillars of Eulerian graph theory”, Euler’s original 1736 paper on the Königsberg bridges problem (which gave the subject its name) and extracts from work of Hierholzer (1873) and Veblen (1931). These are followed by chapters on basic concepts, characterization theorems, generalizations, various types of Eulerian trails, and transformations of Eulerian trails. The style is clear and lively throughout, and the book contains many exercises and a lengthy bibliography.

MSC:

05C45

Eulerian and Hamiltonian graphs

Keywords:

Euclidean graphs; digraphs; Eulerian trail

Citations:

Zbl 0792.05093