Partitioning Perfect Graphs into Stars
  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 same-size stars, 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. 
Ren\'e van Bevern and Robert Bredereck and Laurent Bulteau and Jiehua   Chen and Vincent Froese and Rolf Niedermeier and Ger...
cs.DM cs.DS math.CO