We show that every graph has an induced pseudoforest of at least n−m/4.5
vertices, an induced partial 2-tree of at least n−m/5 vertices, and an
induced planar subgraph of at least n−m/5.2174 vertices. These results are
constructive, implying linear-time algorithms to find the respective induced
subgraphs. We also show that the size of the largest Kh-minor-free graph in
a given graph can sometimes be at most n−m/6+o(m).Comment: Accepted by Graph Drawing 2014. To appear in Journal of Graph
Algorithms and Application