Abstract
We show that for each rational number r such that 4<r⩽5 there exist infinitely many cyclically 4-edge-connected cubic graphs of chromatic index 4 and girth at least 5—that is, snarks—whose flow number equals r. This answers a question posed by Pan and Zhu [Construction of graphs with given circular flow numbers, J Graph Theory 43 [2003], 304–318]. © 2011 Wiley Periodicals, Inc. J Graph Theory 68: 189-201, 2011
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