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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/55463

    Title: Construction of graphs with given circular flow number
    Authors: Pan, Zhi-shi;Zhu, Xu-ding
    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: 2003-08
    Issue Date: 2011-08-22 16:09:00 (UTC+8)
    Publisher: Hoboken: John Wiley & Sons, Inc.
    Abstract: Suppose r ≥ 2 is a real number. A proper r-flow of a directed multi-graph G=(V,E) is a mapping f:E→R such that (i) for every edge e ∈ E ,1 ≤|f(e)| ≤r-1; (ii) for every vertex v ∈V,Σe ∈ E +(v)f(e) =0. 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.
    Relation: Journal of Graph Theory 43(4), pp.304-318
    DOI: 10.1002/jgt.10124
    Appears in Collections:[數學學系暨研究所] 期刊論文

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