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Detecting induced minors in AT-free graphs.

Golovach, P.A. and Kratsch, D. and Paulusma, Daniel (2013) 'Detecting induced minors in AT-free graphs.', Theoretical computer science., 482 . pp. 20-32.


The Induced Minor problem is that of testing whether a graph G can be modified into a graph H by a sequence of vertex deletions and edge contractions. If only edge contractions are permitted, we obtain the Contractibility problem. We prove that Induced Minor is polynomial-time solvable when G is AT-free and H is fixed, i.e., not part of the input. In addition, we show that Contractibility is polynomial-time solvable when G is AT-free and H is a fixed triangle-free graph. We complement these two results by proving that both problems are W[1]-hard on AT-free graphs when parameterized by |VH|.

Item Type:Article
Keywords:Induced minor, Contraction, AT-free graphs.
Full text:(AM) Accepted Manuscript
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Publisher statement:NOTICE: this is the author’s version of a work that was accepted for publication in Theoretical computer science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Theoretical computer science, 482, 22 April 2013, 10.1016/j.tcs.2013.02.029
Date accepted:No date available
Date deposited:19 April 2013
Date of first online publication:April 2013
Date first made open access:No date available

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