Decomposing Cubic Graphs into Connected Subgraphs of Size Three

  • Laurent Bulteau
  • Guillaume Fertin
  • Anthony LabarreEmail author
  • Romeo Rizzi
  • Irena Rusu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9797)


Let \(S=\{K_{1,3},K_3,P_4\}\) be the set of connected graphs of size 3. We study the problem of partitioning the edge set of a graph G into graphs taken from any non-empty \(S'\subseteq S\). The problem is known to be NP-complete for any possible choice of \(S'\) in general graphs. In this paper, we assume that the input graph is cubic, and study the computational complexity of the problem of partitioning its edge set for any choice of \(S'\). We identify all polynomial and NP-complete problems in that setting, and give graph-theoretic characterisations of \(S'\)-decomposable cubic graphs in some cases.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Laurent Bulteau
    • 1
  • Guillaume Fertin
    • 2
  • Anthony Labarre
    • 1
    Email author
  • Romeo Rizzi
    • 3
  • Irena Rusu
    • 2
  1. 1.Université Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE Paris, UPEMMarne-la-ValléeFrance
  2. 2.Laboratoire d’Informatique de Nantes-Atlantique, UMR CNRS 6241Université de NantesNantes Cedex 3France
  3. 3.Department of Computer ScienceUniversity of VeronaVeronaItaly

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