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Planar Induced Subgraphs of Sparse Graphs · arXivDesk

1408.5939Aug 25, 2014Accepted by Graph Drawing 2014. To appear in Journal of Graph Algorithms and Applications

Planar Induced Subgraphs of Sparse Graphs

Glencora Borradaile, David Eppstein, Pingan Zhu

Computational Geometry Data Structures and Algorithms Combinatorics

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 $K_h$

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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.

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Researchers working in cs.CG and adjacent areas.

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The paper addresses: Planar Induced Subgraphs of Sparse Graphs.
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.

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Author comment: Accepted by Graph Drawing 2014. To appear in Journal of Graph Algorithms and Applications

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