JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (12): 17-22.doi: 10.6040/j.issn.1671-9352.0.2017.539

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Linear arboricity of graphs embedded in a surface of non-negative Euler characteristic

CHEN Hong-ling, WANG Hui-juan*, GAO Hong-wei   

  1. School of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong, China
  • Online:2018-12-20 Published:2018-12-18

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Abstract: The linear arboricity of graph G, denoted by la(G), is the minimum number of linear forest required to partition the edge set E(G), which is an improper edge coloring. The linear arboricity of graph which can be embedded in a surface of non-negative Euler characteristic with maximum Δ(G)≥7 is mainly studied. If there is no adjacent chordal 6-cycle, then the arboricity of graph G is「Δ/2.

Key words: Euler characteristic, linear forest, cycle

CLC Number: 

  • O157.5
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