Partitioning perfect graphs into stars. van Bevern, R., Bredereck, R., Bulteau, L., Chen, J., Froese, V., Niedermeier, R., & Woeginger, G. J. Journal of Graph Theory, 85(2):297–335, 2017.
Preprint doi abstract bibtex 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.
@article{BBB+17,
title = {Partitioning perfect graphs into stars},
author = {René van Bevern and Robert Bredereck and Laurent
Bulteau and Jiehua Chen and Vincent Froese and Rolf
Niedermeier and Gerhard J. Woeginger},
url_Preprint = {http://arxiv.org/abs/1402.2589},
doi = {10.1002/jgt.22062},
year = 2017,
date = {2017-06-01},
journal = {Journal of Graph Theory},
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 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.},
volume = 85,
number = 2,
pages = {297--335},
keywords = {algorithmic graph theory}
}
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