Linear 2-arboricity of the complete graph

Chih Hung Yen*, Hung-Lin Fu

*Corresponding author for this work

Research output: Contribution to journalArticle

8 Scopus citations


A linear k-forest is a graph whose components are paths with lengths at most k. The minimum number of linear k-forests needed to decompose a graph G is the linear k-arboricity of G and denoted by lak(G). In this paper, we settle the cases left in determining the linear 2-arboricity of the complete graph Kn. Mainly, we prove that la2(K12t+10) = la2(K12t+11) = 9t + 8 for any t ≥ 0.

Original languageEnglish
Pages (from-to)273-286
Number of pages14
JournalTaiwanese Journal of Mathematics
Issue number1
StatePublished - 1 Jan 2010


  • Complete graph
  • Linear k-arboricity
  • Linear k-forest

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