Partitioning Perfect Graphs into Stars

René van Bevern; Robert Bredereck; Laurent Bulteau; Jiehua Chen; Vincent Froese; Rolf Niedermeier; Gerhard J. Woeginger

doi:10.1002/jgt.22062

Partitioning Perfect Graphs into Stars

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

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

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.

Original language	English
Pages (from-to)	297-335
Number of pages	39
Journal	Journal of Graph Theory
Volume	85
Issue number	2
DOIs	https://doi.org/10.1002/jgt.22062
State	Published - 1 Jun 2017
Externally published	Yes

Keywords

P-Partition
generalized matching problem
graph algorithms
graph factors
graph packing

ASJC Scopus subject areas

Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1002/jgt.22062

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title = "Partitioning Perfect Graphs into Stars",

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.",

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AU - van Bevern, René

AU - Bredereck, Robert

AU - Bulteau, Laurent

AU - Chen, Jiehua

AU - Froese, Vincent

AU - Niedermeier, Rolf

AU - Woeginger, Gerhard J.

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AB - 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.

KW - P-Partition

KW - generalized matching problem

KW - graph algorithms

KW - graph factors

KW - graph packing

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ER -

Partitioning Perfect Graphs into Stars

Abstract

Keywords

ASJC Scopus subject areas

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