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Choosability of toroidal graphs without short cycles
Author(s) -
Cai Leizhen,
Wang Weifan,
Zhu Xuding
Publication year - 2010
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.20460
Subject(s) - combinatorics , mathematics , toroid , chromatic scale , graph , upper and lower bounds , discrete mathematics , physics , mathematical analysis , plasma , quantum mechanics
Let G be a toroidal graph without cycles of a fixed length k , and χ l ( G ) the list chromatic number of G . We establish tight upper bounds of χ l ( G ) for the following values of k :\documentclass{article}\usepackage{amssymb}\usepackage{amsbsy}\usepackage[mathscr]{euscript}\footskip=0pc\pagestyle{empty}\begin{document}\begin{eqnarray*}\chi_l({{G}})\le \left\{\begin{array}{ll}{{4}} & \mbox{if } {{k}}\in \{{{3}},{{4}},{{5}}\} \\{{5}} & \mbox{if } {{k}} = {{6}} \\{{6}} & \mbox{if } {{k}} = {{7}}\end{array}\right.\end{eqnarray*}\end{document} © 2009 Wiley Periodicals, Inc. J Graph Theory 65: 1–15, 2010.