Star Partitions of Perfect Graphs

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

1 SWT - TUB - Department of Software Engineering and Theoretical Computer Science
2 Department of Mathematics and Computer Science, TUE (Eindhoven) and IMAPP, Nijmegen

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, 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-hard cases, for example, on grid graphs and chordal graphs.

Domaines: Algorithme et structure de données [cs.DS]; Complexité [cs.CC]

René van Bevern, Robert Bredereck, Laurent Bulteau, Jiehua Chen, Vincent Froese, et al.. Star Partitions of Perfect Graphs. ICALP, 2014, Copenhague, Denmark. ⟨10.1007/978-3-662-43948-7_15⟩. ⟨hal-01260593⟩