Cookies

We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.


Durham Research Online
You are in:

Detecting induced minors in AT-free graphs.

Golovach, P.A and Kratsch, D. and Paulusma, Daniel (2012) 'Detecting induced minors in AT-free graphs.', in Algorithms and computation : 23rd International Symposium, ISAAC 2012, Taipei, Taiwan, 19-21 December 2012 ; proceedings. Berlin ; Heidelberg: Springer, pp. 495-505. Lecture notes in computer science., 7676 (7676).

Abstract

The problem Induced Minor is to test whether a graph G can be modified into a graph H by a sequence of vertex deletions and edge contractions. 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. Our result can be considered to be optimal in some sense as we also prove that Induced Minor is W[1]-hard on AT-free graphs, when parameterized by |VH|. In order to obtain it we prove that the Set-Restricted k-Disjoint Paths problem can be solved in polynomial time on AT-free graphs for any fixed k. We also use the latter result to prove that the Set-Restricted k-Disjoint Connected Subgraphs problem is polynomial-time solvable on AT-free graphs for any fixed k.

Item Type:Book chapter
Full text:Full text not available from this repository.
Publisher Web site:http://dx.doi.org/10.1007/978-3-642-35261-4_52
Date accepted:No date available
Date deposited:No date available
Date of first online publication:2012
Date first made open access:No date available

Save or Share this output

Export:
Export
Look up in GoogleScholar