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Snarks with given real flow numbers
Author(s) -
Lukot'ka Robert,
Škoviera Martin
Publication year - 2011
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20551
Subject(s) - mathematics , combinatorics , graph , girth (graph theory) , cubic graph , discrete mathematics , chromatic scale , flow (mathematics) , edge coloring , line graph , graph power , voltage graph , geometry
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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