Dirac's map-color theorem for choosability

It is proved that the choice number of every graph G embedded on a surface of Euler genus ε ≥ 1 and ε ≠ 3 is at most the Heawood number $H(\epsilon)= \lfloor(7+\sqrt{24\epsilon+1})/2\rfloor$ and that the equality holds if and only if G contains the complete graph KH(ε) as a subgraph. © 1999 John Wil...

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Bibliographic Details
Published inJournal of graph theory Vol. 32; no. 4; pp. 327 - 339
Main Authors Böhme, T., Mohar, B., Stiebitz, M.
Format Journal Article
LanguageEnglish
Published New York John Wiley & Sons, Inc 01.12.1999
Subjects
choosability
critical graph
graph coloring
Heawood number
list-coloring
projective plane
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Summary:It is proved that the choice number of every graph G embedded on a surface of Euler genus ε ≥ 1 and ε ≠ 3 is at most the Heawood number $H(\epsilon)= \lfloor(7+\sqrt{24\epsilon+1})/2\rfloor$ and that the equality holds if and only if G contains the complete graph KH(ε) as a subgraph. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 327–339, 1999
Bibliography:ArticleID:JGT2
istex:76BD2D26B09B23C3C388B3A7DAAA9804B4176799
ark:/67375/WNG-T3B8NRVL-W
ISSN:0364-9024
1097-0118
DOI:10.1002/(SICI)1097-0118(199912)32:4<327::AID-JGT2>3.0.CO;2-B