Abstract
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 K h -minor-free graph in a given graph can sometimes be at most n − m/6 + o(m).
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Borradaile, G., Eppstein, D., Zhu, P. (2014). Planar Induced Subgraphs of Sparse Graphs. In: Duncan, C., Symvonis, A. (eds) Graph Drawing. GD 2014. Lecture Notes in Computer Science, vol 8871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45803-7_1
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