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不含4-圈和5-圈的平面图的线性2-荫度 被引量：4

The linear 2-arboricity of plane graphs without 4-cycles and 5-cycles
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摘要 线性k-森林是每一个连通分支均为长度不超过k的路的图。一个图G的线性k-荫度是将图G的边集合能分解成的线性k-森林的最少数目,用lak(G)来表示。证明了:若G为不含4-圈和5-圈的平面图,则la2(G)≤「Δ(G)+1/2■+4。 A linear k-forest is a forest whose components are paths of length at most k.The linear k-arboricity of a graph G,denoted by lak（G）,is the least number of linear k-forests needed to decompose G.We have： if G is a plane graph without 4-cycles and 5-cycles,then la2（G）≤「Δ（G）＋1/2■＋4.
作者 王苒群 左连翠
机构地区 天津师范大学数学科学学院
出处 《山东大学学报（理学版）》 CAS CSCD 北大核心 2012年第6期71-75,共5页 Journal of Shandong University(Natural Science)
基金 国家自然科学基金青年基金资助项目(61103073)
关键词 线性k-森林 线性k-荫度 线性荫度 平面图 linear k-forest linear k-arboricity linear arboricity plane graph
分类号 O157 [理学—基础数学]
  • 相关文献

参考文献14

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  • 2HABIB M, PEROCHE B. Some problems about linear arboricity[ J ]. Disc Math, 1982, 41:219-220.
  • 3BERMOND J C, FIUQUET J L, HABIB M, et al. On linear k-arboricity [ J ]. Discrete Math. , 1984, 52:123-132.
  • 4JACKSON B, WORMALD N C. On the linear k-arboricity of cubic graphs[ J ]. Disc Math, 1996, 162:293-297.
  • 5ALDRED R E L, WORMALD N C. More on the linear k-arboricity of regular graphs[ J ]. Austral J Combin, 1998, 18:97- 104.
  • 6FU Hung-Lin, HUANG Kuo-Ching. The linear 2-arboricity of complete bipartite graphs[ J ]. Ars Combin, 1994, 38:309-318.
  • 7CHEN Bor-Liang, FU Hung-Lin, HUANG Kuo-Ching. Decomposing graphs into forests of paths with size less than three[ J ]. Austral J Combin, 1991, 3:55-73.
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同被引文献15

  • 1钱景,王维凡.不含4-圈的平面图的线性2-荫度[J].浙江师范大学学报（自然科学版）,2006,29(2):121-125. 被引量：4
  • 2BONDYJA,MURTYUUSR.Graphtheorywithapplication[M].NewYork:MacMillanPress,1976.
  • 3HABIBM,PEROCHEB.Someproblemsaboutlineararboricity[J].DiscreteMath,1982,41:219-220.
  • 4BERMONDJC,FIUQUETJL,HABIBM,etal.Onlinearkarboridty[J].DiscreteMath,1984,52:123-132.
  • 5JACKSONB,WORMALDNC.Onthelinearkarborictyofcubicgraphs[J].DiscreteMath,1996,162:293-297.
  • 6ALDREDREL,WORMALDNC.Moreonthelinearkarboricityofregulargraphs[J].AustralJCombin,1998,18:97-104.
  • 7FUHungLin,HUANGKuoChing.Thelinear2-arboricityofcompletebipartitegraphs[J].ArsCombin,1994,38:309-318.
  • 8CHENBorLiang,FUHungLin,HUANGKuoChing.Decomposinggraphsintoforestsofpathwithsizelessthanthree[J].AustralJCombin,1991,3:55-73.
  • 9YENChihHung,FUHungLin.Linear2-arboricityofthecompletegraph[J].TaiwaneseJMath,2010,14(1):273-286.
  • 10THOMASSENC.Twocoloringtheedgesofacubicgraphsuchthateachmonochromaticcomponentisapathoflengthatmost5[J].JCombinTheory:SerB,1999,75:100109.

引证文献4

二级引证文献4

山东大学学报（理学版）
2012年 第6期

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