The induced h -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 induced h -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-hardness of induced h -matching for graphs excluding k 1,4 as an induced subgraph. In particular, we show that independent set is w-hard on k 1,4-free graphs.
|Title of host publication||Algorithms - ESA 2012|
|Subtitle of host publication||20th Annual European Symposium Ljubljana, Slovenia, September 2012 Proceedings|
|Editors||Leah Epstein, Paolo Ferragina|
|Publication status||Published - 2012|
|Series||Lecture Notes in Computer Science|
Hermelin, D., Mnich, M., & van Leeuwen, E. J. (2012). Parameterized Complexity of Induced H-Matching on Claw-Free Graphs. In L. Epstein, & P. Ferragina (Eds.), Algorithms - ESA 2012: 20th Annual European Symposium Ljubljana, Slovenia, September 2012 Proceedings (pp. 624-635). Springer. Lecture Notes in Computer Science, Vol.. 7501 https://doi.org/10.1007/978-3-642-33090-2_54