Partitioning perfect graphs into stars. van Bevern, R., Bredereck, R., Bulteau, L., Chen, J., Froese, V., Niedermeier, R., & Woeginger, G. J. Journal of Graph Theory, 85(2):297–335, 2017.
Partitioning perfect graphs into stars [link]Preprint  doi  abstract   bibtex   
The partition of graphs into nice subgraphs is a central algorithmic problem with strong ties to matching theory. We study the partitioning of undirected graphs into stars of the same size, a problem known to be NP-complete even for the case of stars on three vertices. We perform a thorough computational complexity study of the problem on subclasses of perfect graphs and identify several polynomial-time solvable cases, for example, on interval graphs and bipartite permutation graphs, and also NP-complete cases, for example, on grid graphs and chordal graphs.
@article{BBB+17,
  title =	 {Partitioning perfect graphs into stars},
  author =	 {René van Bevern and Robert Bredereck and Laurent
                  Bulteau and Jiehua Chen and Vincent Froese and Rolf
                  Niedermeier and Gerhard J. Woeginger},
  url_Preprint = {http://arxiv.org/abs/1402.2589},
  doi =		 {10.1002/jgt.22062},
  year =	 2017,
  date =	 {2017-06-01},
  journal =	 {Journal of Graph Theory},
  abstract =	 {The partition of graphs into nice subgraphs is a
                  central algorithmic problem with strong ties to
                  matching theory. We study the partitioning of
                  undirected graphs into stars of the same size, a
                  problem known to be NP-complete even for the case of
                  stars on three vertices. We perform a thorough
                  computational complexity study of the problem on
                  subclasses of perfect graphs and identify several
                  polynomial-time solvable cases, for example, on
                  interval graphs and bipartite permutation graphs,
                  and also NP-complete cases, for example, on grid
                  graphs and chordal graphs.},
  volume =	 85,
  number =	 2,
  pages =	 {297--335},
  keywords =	 {algorithmic graph theory}
}

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