Construction of graphs with given circular flow number.

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Title:	Construction of graphs with given circular flow number.
Authors:	潘志實
Contributors:	淡江大學數學學系
Keywords:	graph;flow;circular flow number;rooted-flow;series join;parallel join;two-terminal graph
Date:	2003-07-07
Issue Date:	2011-10-01 21:04:36 (UTC+8)
Abstract:	Suppose r ≥ 2 is a real number. A proper r-flow of a directed multi-graph equation image is a mapping equation image such that (i) for every edge equation image, equation image; (ii) for every vertex equation image, equation image. The circular flow number of a graph G is the least r for which an orientation of G admits a proper r-flow. The well-known 5-flow conjecture is equivalent to the statement that every bridgeless graph has circular flow number at most 5. In this paper, we prove that for any rational number r between 2 and 5, there exists a graph G with circular flow number r. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 304–318, 2003
Relation:	J. Graph Theory 43,　p.304-318
DOI:	10.1002/jgt.10124
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

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