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arXiv · 1408.5939

Planar Induced Subgraphs of Sparse Graphs

Glencora Borradaile·David Eppstein·Pingan Zhu
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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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Glencora Borradaile, David Eppstein, Pingan Zhu. 2015-05-12. Planar Induced Subgraphs of Sparse Graphs. https://doi.org/10.7155/jgaa.00358

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