Abstract
A graph is l-apex if it can be made planar by removing at most l vertices. In this paper we show that the vertex set of any graph not containing an l-apex graph as a minor can be partitioned in linear time into 2 l sets inducing graphs with small treewidth. As a consequence, several maximum induced-subgraph problems when restricted to graph classes not containing some special l-apex graphs as minors, have practical approximation algorithms.
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