TY - JOUR
T1 - Parameterized complexity of induced graph matching on claw-free graphs
AU - Hermelin, Danny
AU - Mnich, Matthias
AU - Van Leeuwen, Erik Jan
N1 - Funding Information:
An extended abstract of the results in this paper have appeared in the Proceedings of 20th European Symposium on Algorithms (ESA 2012) []. Partially supported by ERC StG project PAAl No. 259515. The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007–2013) under REA grant agreement No. 631163.11.
PY - 2014/1/1
Y1 - 2014/1/1
N2 - The Induced Graph Matching problem asks to find k disjoint induced subgraphs isomorphic to a given graph H in a given graph G such that there are no edges between vertices of different subgraphs. This problem generalizes the classical Independent Set and Induced Matching problems, among several other problems. We show that Induced Graph Matching is fixed-parameter tractable in k on claw-free graphs when H is a fixed connected graph, and even admits a polynomial kernel when H is a complete graph. Both results rely on a new, strong, and generic algorithmic structure theorem for claw-free graphs. Complementing the above positive results, we prove W[1] -hardness of Induced Graph Matching on graphs excluding K1,4 as an induced subgraph, for any fixed complete graph H. In particular, we show that Independent Set is W[1] -hard on K1,4-free graphs. Finally, we consider the complexity of Induced Graph Matching on a large subclass of claw-free graphs, namely on proper circular-arc graphs. We show that the problem is either polynomial-time solvable or NP-complete, depending on the connectivity of H and the structure of G.
AB - The Induced Graph Matching problem asks to find k disjoint induced subgraphs isomorphic to a given graph H in a given graph G such that there are no edges between vertices of different subgraphs. This problem generalizes the classical Independent Set and Induced Matching problems, among several other problems. We show that Induced Graph Matching is fixed-parameter tractable in k on claw-free graphs when H is a fixed connected graph, and even admits a polynomial kernel when H is a complete graph. Both results rely on a new, strong, and generic algorithmic structure theorem for claw-free graphs. Complementing the above positive results, we prove W[1] -hardness of Induced Graph Matching on graphs excluding K1,4 as an induced subgraph, for any fixed complete graph H. In particular, we show that Independent Set is W[1] -hard on K1,4-free graphs. Finally, we consider the complexity of Induced Graph Matching on a large subclass of claw-free graphs, namely on proper circular-arc graphs. We show that the problem is either polynomial-time solvable or NP-complete, depending on the connectivity of H and the structure of G.
KW - Algorithms and data structures
KW - Claw-free graphs
KW - Fixed-parameter tractability
KW - Induced matchings
UR - http://www.scopus.com/inward/record.url?scp=84896691879&partnerID=8YFLogxK
U2 - 10.1007/s00453-014-9877-5
DO - 10.1007/s00453-014-9877-5
M3 - Article
AN - SCOPUS:84896691879
SN - 0178-4617
VL - 70
SP - 513
EP - 560
JO - Algorithmica
JF - Algorithmica
IS - 3
ER -