The Two-Coloring Number and Degenerate Colorings of Planar Graphs

  • Authors:

  • Hal Kierstead;Bojan Mohar;Simon Špacapan;Daqing Yang;Xuding Zhu

  • Affiliations:

  • kierstead@asu.edu;mohar@sfu.ca;simon.spacapan@uni-mb.si;daqing85@yahoo.com;zhu@math.nsysu.edu.tw

  • Venue:
  • SIAM Journal on Discrete Mathematics
  • Year:
  • 2009

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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 the 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.