Partitioning Perfect Graphs into Stars1. Issue 2 (15th June 2016)

• Record Type: Journal Article
• Authors: van Bevern, René; Bredereck, Robert; Bulteau, Laurent; Chen, Jiehua; Froese, Vincent; Niedermeier, Rolf; Woeginger, Gerhard J.
• Is Part Of: Journal of graph theory. Volume 85:Issue 2(2017)
• Page Start: 297
• Page End: 335
• Publication Date: 2016-06-15
• Subjects: P3‐Partition -- generalized matching problem -- graph factors -- graph packing -- graph algorithms; Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.22062
• Languages: English
• ISSNs: 0364-9024

Abstract

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 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.