On the induced matching problem

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Abstract

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(91k+n) whether a planar graph contains an induced matching of size at least k.

Keywords

Induced matching
Planar graphs
Outerplanar graphs
Kernel
Parameterized algorithms
Twins

Cited by (0)

A preliminary version of this paper appeared in STACS, 2008, pp. 397–408.

1

This work was supported in part by a DePaul University Competitive Research Grant.

2

Partially supported by NSA Grant H98230-08-1-0043.

3

The work of this author was supported in part by a Lafayette College research grant.