Partitioning Perfect Graphs into Stars

René van Bevern (1) , Robert Bredereck (1) , Laurent Bulteau (1, 2) , Jiehua Chen (3) , Vincent Froese (1) , Rolf Niedermeier (1) , Gerhard J. Woeginger (4)

1 SWT - TUB - Department of Software Engineering and Theoretical Computer Science
2 LIGM - Laboratoire d'Informatique Gaspard-Monge
3 NPU - Northwestern Polytechnical University [Xi'an]
4 Department of mathematics and computing science [Eindhoven]

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.

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

René van Bevern, Robert Bredereck, Laurent Bulteau, Jiehua Chen, Vincent Froese, et al.. Partitioning Perfect Graphs into Stars. Journal of Graph Theory, 2017, 85 (2), pp.297-335. ⟨10.1002/jgt.22062⟩. ⟨hal-01494420⟩