The Two-Coloring number and degenerate colorings of planar graphs

Henry Kierstead, Bojan Mohar, Simon Špacapan, Daqing Yang, Xuding Zhiu

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The two-coloring number of graphs, which was originally introduced in the study of the game chromatic number, also gives an upper bound on t he degenerate chromatic number as introduced by Borodin. It is proved that the two-coloring number of any planar graph is at most nine. As a consequence, the degenerate list chromatic number of any planar graph is at most nine. It is also shown that the degenerate diagonal chromatic number is at most 11 and the degenerate diagonal list chromatic number is at most 12 for all planar graphs.

Original languageEnglish (US)
Pages (from-to)1548-1560
Number of pages13
JournalSIAM Journal on Discrete Mathematics
Volume23
Issue number3
DOIs
StatePublished - 2009

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Chromatic number
Planar graph
Colouring
Game Chromatic number
Upper bound
Graph in graph theory

Keywords

  • Degenerate coloring
  • Planar graph
  • Two-coloring number

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The Two-Coloring number and degenerate colorings of planar graphs. / Kierstead, Henry; Mohar, Bojan; Špacapan, Simon; Yang, Daqing; Zhiu, Xuding.

In: SIAM Journal on Discrete Mathematics, Vol. 23, No. 3, 2009, p. 1548-1560.

Research output: Contribution to journalArticle

Kierstead, Henry ; Mohar, Bojan ; Špacapan, Simon ; Yang, Daqing ; Zhiu, Xuding. / The Two-Coloring number and degenerate colorings of planar graphs. In: SIAM Journal on Discrete Mathematics. 2009 ; Vol. 23, No. 3. pp. 1548-1560.
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