LIPIcs.STACS.2012.182.pdf
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Contraction checking in graphs on surfaces
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29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS) - License:
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
- Publication Date: 2012-02-24
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Marcin Kaminski and Dimitrios M. Thilikos. Contraction checking in graphs on surfaces. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 182-193, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)
https://doi.org/10.4230/LIPIcs.STACS.2012.182
https://doi.org/10.4230/LIPIcs.STACS.2012.182
Abstract
The Contraction Checking problem asks, given two graphs H and G as input, whether H can be obtained from G by a sequence of edge contractions. Contraction Checking remains NP-complete, even when H is fixed. We show that this is not the case when G is embeddable in a surface of fixed Euler genus. In particular, we give an algorithm that solves Contraction Checking in f(h,g)*|V(G)|^3 steps, where h is the size of H and g is the Euler genus of the input graph G.
Keywords
- Surfaces
- Topological Minors
- Contractions
- Parameterized algorithms
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