JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (12): 31-40.doi: 10.6040/j.issn.1671-9352.0.2017.642

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Planar graphs without 4-cycle or chordal-6-cycle are(3,0,0)-colorable

LIU Jia, SUN Lei*   

  1. School of Mathematics and statistics, Shandong Normal University, Jinan 250014, Shandong, China
  • Online:2018-12-20 Published:2018-12-18

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Abstract: Let d1,d2,…,dk be k non-negative intergers. A graph G is(d1,d2,…,dk)-colorable, if the vertex set of G can be partitioned into subsets V1,V2,…,Vk such that the graph G［Vi］ induced by Vi has maximum degree at most di for i=1,2,…,k. There is a conclusion about the coloring of planar graphs: planar graphs without 4-cycle or chordal-6-cycle are(3,0,0)-colorable.

Key words: planar graph, improper coloring, cycle, chordal-6-cycle

CLC Number: 

  • O157.5
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