JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (12): 36-41.doi: 10.6040/j.issn.1671-9352.0.2016.597

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Linear 2-arboricity of planar graphs with 4-cycles have no common vertex

CHEN Hong-yu1, ZHANG Li2   

  1. 1. School of Science, Shanghai Institute of Technology, Shanghai 201418, China;
    2. School of Statistics and Mathematics, Shanghai Lixin University of Accouting and Finance, Shanghai 201209, China
  • Received:2016-12-16 Online:2017-12-20 Published:2017-12-22

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Abstract: The linear 2-arboricity la2(G)of G is the least integer k to divide G into k edge-disjoint forests, and each branch of the forests is a path with the length at most 2. We prove that if G is a planar graph with 4-cycles without common vertex, then la2(G)≤「Δ/2+5.

Key words: cycle, planar graph, linear 2-arboricity

CLC Number: 

  • O157.5
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