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Graphs and Combinatorics

, Volume 29, Issue 4, pp 1113–1124 | Cite as

Linear Coloring of Planar Graphs Without 4-Cycles

  • Weifan WangEmail author
  • Yiqiao Wang
Original Paper
  • 162 Downloads

Abstract

A proper vertex coloring of a graph G is linear if the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc(G) of G is the smallest number of colors in a linear coloring of G. In this paper, we prove that if G is a planar graph without 4-cycles, then lc\({(G)\le \lceil \frac {\Delta}2\rceil+8}\) , where Δ denotes the maximum degree of G.

Keywords

Linear coloring Planar graph Cycle Maximum degree 

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Copyright information

© Springer 2012

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang Normal UniversityJinhuaChina
  2. 2.Academy of Mathematics and Systems ScienceBeijingChina

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