(Δ+1)-total-colorability of plane graphs with maximum degree Δ at least 6 and without adjacent short cycles

Authors:
Jingwen Zhang;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
Venue:
Information Processing Letters
Year:
2010

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Abstract

By a short cycle we mean a cycle of length at most 4. In this paper, we prove that every plane graph with maximum degree @D at least 6 and without adjacent short cycles is (@D+1)-totally-colorable.