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Three-regular Subgraphs of Four-regular Graphs

✍ Scribed by O. Moreno; V.A. Zinoviev

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 85 KB
Volume: 19
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1997.0150

No coin nor oath required. For personal study only.

✦ Synopsis

For any 4-regular graph G (possibly with multiple edges), we prove that, if the number N of distinct Euler orientations of G is such that N ≡ 1 (mod 3), then G has a 3-regular subgraph. It gives the new 4-regular graphs with multiple edges which have no 3-regular subgraphs, for which we know the number of Euler orientations.

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