Planar graphs with maximum degree 8 and without adjacent triangles are 9-totally-colorable

Authors:
Dingzhu Du;Lan Shen;Yingqian Wang
Affiliations:
College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Zhejiang Jinhua 321004, China;College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Zhejiang Jinhua 321004, China;College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Zhejiang Jinhua 321004, China
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

The Total Coloring Conjecture, in short, TCC, says that every simple graph is (@D+2)-totally-colorable where @D is the maximum degree of the graph. Even for planar graphs this conjecture has not been completely settled yet. However, every planar graph with @D=9 has been proved to be (@D+1)-totally-colorable. In this paper, we prove that planar graphs with maximum degree 8 and without adjacent triangles are 9-totally-colorable.