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An Eulerian exposition

Linda Lesniak, Ortrud R. Oellermann

Abstract

Abstract An overview of Eulerian graphs is presented. In particular, characterizations of Eulerian graphs and digraphs as well as algorithms for constructing Eulerian circuits are discussed. A solution to the Chinese postman problem is followed by a study of subgraphs and supergraphs of Eulerian graphs. After an introduction to randomly Eulerian graphs and digraphs, we conclude with a summary of a variety of results involving enumeration.

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Key concepts: Eulerian path, Mathematics, Exposition (narrative), Combinatorics, Discrete mathematics, Applied mathematics, Literature, Art