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The linear 2-arboricity of planar graphs without 5-, 6-cycles with chord

CHEN Hong-yu1, ZHANG Li2   

  1. 1. School of Science, Shanghai Institute of Technology, Shanghai 201418, China;
    2. Department of Applied Mathematics, Shanghai Finance University, Shanghai 201209,  China
  • Received:2013-03-06 Online:2014-06-20 Published:2014-06-14

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Abstract: Let G be a planar graph without 5-,6-cycles with chord. It is proved that if G is connected and  δ(G)≥2, than G contains an edge xy with d(x)+d(y)≤9 or a 2alternating cycle. By this result, we obtain that G-s linear 2-arboricity la2(G)≤Δ(G)2+6.

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

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