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Circular flow numbers of regular multigraphs

✍ Scribed by Eckhard Steffen

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 177 KB
Volume: 36
Category: Article
ISSN: 0364-9024
DOI: 10.1002/1097-0118(200101)36:1<24::aid-jgt3>3.0.co;2-q

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✦ Synopsis

The circular ¯ow number F c (G) of a graph G (V,E) is the minimum r P Q such that G admits a ¯ow 0 with 1 0 (e) r À 1, for each e P E. We determine the circular ¯ow number of some regular multigraphs. In particular, we characterize the bipartite (2t 1)-regular graphs (t ! 1). Our results imply that there are gaps for possible circular ¯ow numbers for (2t 1)-regular graphs, e.g., there is no cubic graph G with 3 < F c (G) < 4. We further show that there are snarks with circular ¯ow number arbitrarily close to 4, answering a question of X. Zhu.

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