Obtaining Planarity by Contracting Few Edges
Petr A. Golovach, Pim van 't Hof, Daniel Paulusma
TL;DR
This paper proves that determining whether a graph can be made planar through a limited number of edge contractions is fixed-parameter tractable, despite the problem's NP-completeness.
Contribution
It establishes the fixed-parameter tractability of the Planar Contraction problem parameterized by the number of edge contractions k.
Findings
The problem is NP-complete in general.
The problem is fixed-parameter tractable when parameterized by k.
Provides an algorithmic approach for small k values.
Abstract
The Planar Contraction problem is to test whether a given graph can be made planar by using at most k edge contractions. This problem is known to be NP-complete. We show that it is fixed-parameter tractable when parameterized by k.
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Optimization and Search Problems