Planar graphs without cycles of length from 4 to 7 are 3-colorable

Planar graphs without cycles of length from 4 to 7 are 3-colorable

Planar graphs without cycles of length from 4 to 7 are proved to be 3-colorable. Moreover, it is proved that each proper 3-coloring of a face of length from 8 to 11 in a connected plane graph without cycles of length from 4 to 7 can be extended to a proper 3-coloring of the whole graph. This improve...

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Veröffentlicht in:Journal of combinatorial theory. Series B 2005, Vol.93 (2), p.303-311
Hauptverfasser: Borodin, O.V., Glebov, A.N., Raspaud, A., Salavatipour, M.R.
Format: Artikel
Sprache:eng
Schlagworte:
3-coloring
Computer Science
Other
Planar graphs
Steinberg's conjecture
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Zusammenfassung:Planar graphs without cycles of length from 4 to 7 are proved to be 3-colorable. Moreover, it is proved that each proper 3-coloring of a face of length from 8 to 11 in a connected plane graph without cycles of length from 4 to 7 can be extended to a proper 3-coloring of the whole graph. This improves on the previous results on a long standing conjecture of Steinberg.
ISSN:0095-8956
1096-0902
DOI:10.1016/j.jctb.2004.11.001