JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (8): 100-106.doi: 10.6040/j.issn.1671-9352.0.2016.363

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Total coloring of planar graphs with maximum degree seven

WANG Xiao-li1, WANG Hui-juan2*, LIU Bin1   

  1. 1. School of Mathematical Sciences, Ocean University of China, Qingdao 266100, Shandong, China;
    2. School of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong, China
  • Received:2016-07-23 Online:2017-08-20 Published:2017-08-03

Abstract: Let G be a planar graph with maximum degree Δ≥7. It is proved that if chordal 5-cycles of G are not adjacent to chordal 6-cycles, then its total chromatic number is Δ+1 by the discharging method.

Key words: total coloring, cycle, planar graph, discharging

CLC Number: 

  • O157.5
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