Planar Induced Subgraphs of Sparse Graphs

  • Glencora Borradaile
  • David Eppstein
  • Pingan Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8871)

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 Kh-minor-free graph in a given graph can sometimes be at most n − m/6 + o(m).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Glencora Borradaile
    • 1
  • David Eppstein
    • 2
  • Pingan Zhu
    • 1
  1. 1.Oregon State UniversityCorvallisUSA
  2. 2.University of CaliforniaIrvineUSA

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