(Δ+1)-total-colorability of plane graphs of maximum degree Δ≥6 with neither chordal 5-cycle nor chordal 6-cycle

Authors:
Qian Wu;Qiuli Lu;Yingqian Wang
Affiliations:
College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China;College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China;College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China
Venue:
Information Processing Letters
Year:
2011

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Abstract

In this paper, we prove that a plane graph of maximum degree @D=6 is (@D+1)-totally-colorable if it contains neither chordal 5-cycle nor chordal 6-cycle. This further extends the known class of plane graphs of maximum degree @D in which every graph is (@D+1)-totally-colorable.