Packing [1, Delta] -factors in graphs of small degree

  title={Packing [1, Delta] -factors in graphs of small degree},
  author={Adrian Kosowski and Michal Malafiejski and Pawel Zylinski},
  journal={J. Comb. Optim.},
Given an undirected, connected graph G with maximum degree , we introduce the concept of a [1, ]-factor k-packing in G, defined as a set of k edgedisjoint subgraphs of G such that every vertex of G has an incident edge in at least one subgraph. The problem of deciding whether a graph admits a [1, ]-factor kpacking is shown to be solvable in linear time for k = 2, but NP-complete for all k ≥ 3. For k = 2, the optimisation problem of minimising the total number of edges of the subgraphs of the… CONTINUE READING