Operations Research Transactions ›› 2019, Vol. 23 ›› Issue (2): 113-119.doi: 10.15960/j.cnki.issn.1007-6093.2019.02.011

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The linear aboricity of planar graphs with 6-cycles containing at most one chord

LUO Zhaoyang*, SUN Lin   

  1. Department of Mathematics, Changji University, Changji 831100, Xinjiang, China
  • Received:2017-03-09 Online:2019-06-15 Published:2019-06-15

Abstract: The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. In this paper, using the discharging method, it is proved that for a planar graph G, la(G)=「△(G)/2」 if △(G) > 7 and every 6-cycle of G contains at most one chord.

Key words: cycle, planar graph, linear arboricity, discharging method

CLC Number: