Planarization of Graphs Embedded on Surfaces
WG '95 Proceedings of the 21st International Workshop on Graph-Theoretic Concepts in Computer Science
Induced Matchings in Regular Graphs and Trees
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Maximum Induced Linear Forests in Outerplanar Graphs
Graphs and Combinatorics
Extremal Combinatorics: With Applications in Computer Science
Extremal Combinatorics: With Applications in Computer Science
Induced packing of odd cycles in planar graphs
Theoretical Computer Science
When is weighted satisfiability FPT?
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Maximum matching in multi-interface networks
Theoretical Computer Science
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We study extremal questions on induced matchings in certain natural graph classes. We argue that these questions should be asked for twinless graphs, that is graphs not containing two vertices with the same neighborhood. We show that planar twinless graphs always contain an induced matching of size at least n/40 while there are planar twinless graphs that do not contain an induced matching of size (n+10)/27. We derive similar results for outerplanar graphs and graphs of bounded genus. These extremal results can be applied to the area of parameterized computation. For example, we show that the induced matching problem on planar graphs has a kernel of size at most 40k that is computable in linear time; this significantly improves the results of Moser and Sikdar (2007). We also show that we can decide in time O(91^k+n) whether a planar graph contains an induced matching of size at least k.