RenĂ© van Bevern, Robert Bredereck, Laurent Bulteau, Jiehua Chen, Vincent Froese, Rolf Niedermeier, and Gerhard J. Woeginger. Partitioning perfect graphs into stars. Journal of Graph Theory, 85(2):297–335, 2017.

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.

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