A status on the linear arboricity

  • J. Akiyama
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 108)


In a inear forest, each component is a path. The linear arboricity ≡(G) of a graph G is defined in Harary [8] as the minimum number of linear forests whose union is G. This invariant first arose in a study [10] of information retrieval in file systems. A quite similar covering invariant which is well known to the linear arboricity is the arboricity of a graph, which is defined as the minimum number of forests whose union is G. Nash-Williams [11] determined the arboricity of any graph, however only few results on the linear arboricity are known. We shall present these discoveries and an open problem on this new invariant.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • J. Akiyama
    • 1
  1. 1.Department of MathematicsNippon Ika UniversityKawasakiJapan

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