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Nowhere-zero 4-flows and cycle double covers

✍ Scribed by Cun-Quan Zhang

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 572 KB
Volume: 154
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00047-z

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✦ Synopsis

In this paper, we obtained some necessary and sufficient conditions for a graph having 5, 6and 7-cycle double covers, etc. We also provide a few necessary and sufficient conditions for a graph admitting a nowhere-zero 4-flow. With the aid of those basic properties of nowhere-zero 4flow and the result about 5-cycle double cover, we are able to prove that each 2-edge-connected graph with one edge short of admitting a nowhere-zero 4-flow has a 5-cycle double cover which is a generalization of a theorem due to Huck and Koch01 (JCTB, 1995) for cubic graphs.

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