Decomposing Subcubic Graphs into Claws, Paths or Triangles

Laurent Bulteau (1, 2) , Guillaume Fertin (3, 4) , Anthony Labarre (1) , Romeo Rizzi (5) , Irena Rusu (4)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 CNRS - Centre National de la Recherche Scientifique
3 LS2N - équipe COMBI - Combinatoire et Bioinformatique
4 LS2N - Laboratoire des Sciences du Numérique de Nantes
5 UNIVR | DI - Department of Computer Science [Verona]

Let S = {K1,3, K3, P4} 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 ⊆ 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 subcubic (i.e. all its vertices have degree at most 3), 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.

Mots clés: decomposition; edge partition; NP-completeness; subcubic graph; decomposition

Domaines: Complexité [cs.CC]; Bio-informatique [q-bio.QM]; Algorithme et structure de données [cs.DS]

Laurent Bulteau, Guillaume Fertin, Anthony Labarre, Romeo Rizzi, Irena Rusu. Decomposing Subcubic Graphs into Claws, Paths or Triangles. Journal of Graph Theory, 2021, 98 (4), pp.557-588. ⟨10.1002/jgt.22713⟩. ⟨hal-03388424⟩