Journal of the ACM (JACM)
Selected papers from the second Krakow conference on Graph theory
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Theoretical Computer Science - Parameterized and exact computation
Journal of Graph Theory
Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems
Algorithmica - Parameterized and Exact Algorithms
Bounding χ in terms of ω and Δ for quasi-line graphs
Journal of Graph Theory
On the parameterized complexity of multiple-interval graph problems
Theoretical Computer Science
A Problem Kernelization for Graph Packing
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Domination when the stars are out
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Dominating set is fixed parameter tractable in claw-free graphs
Theoretical Computer Science
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Kernelization of packing problems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Weak compositions and their applications to polynomial lower bounds for kernelization
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Efficient approximation schemes for geometric problems?
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Induced disjoint paths in AT-Free graphs
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Induced disjoint paths in claw-free graphs
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Parameterized Complexity
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The InducedH-Matching problem asks to find k disjoint, induced subgraphs isomorphic to H in a given graph G such that there are no edges between vertices of different subgraphs. This problem generalizes amongst others the classical Independent Set and Induced Matching problems. We show that InducedH-Matching is fixed-parameter tractable in k on claw-free graphs when H is a fixed connected graph of constant size, and even admits a polynomial kernel when H is a clique. Both results rely on a new, strong algorithmic structure theorem for claw-free graphs. To show the fixed-parameter tractability of the problem, we additionally apply the color-coding technique in a nontrivial way. Complementing the above two positive results, we prove the W[1]-hardness of InducedH-Matching for graphs excluding K1,4 as an induced subgraph. In particular, we show that Independent Set is W[1]-hard on K1,4-free graphs.