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Operations Research Transactions >

2019 , Vol. 23 >Issue 2: 113 - 119

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2019.02.011

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

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  • Department of Mathematics, Changji University, Changji 831100, Xinjiang, China

Received date: 2017-03-09

  Online published: 2019-06-15

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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

Cite this article

LUO Zhaoyang, SUN Lin . The linear aboricity of planar graphs with 6-cycles containing at most one chord[J]. Operations Research Transactions, 2019 , 23(2) : 113 -119 . DOI: 10.15960/j.cnki.issn.1007-6093.2019.02.011

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