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Dense Induced Bipartite Subgraphs in Triangle-Free Graphs

  • Matthew KwanEmail author
  • Shoham LetzterEmail author
  • Benny SudakovEmail author
  • Tuan TranEmail author
Article
  • 15 Downloads

Abstract

The problem of finding dense induced bipartite subgraphs in H-free graphs has a long history, and was posed 30 years ago by Erdős, Faudree, Pach and Spencer. In this paper, we obtain several results in this direction. First we prove that any H-free graph with minimum degree at least d contains an induced bipartite subgraph of minimum degree at least cH log d/log log d, thus nearly confirming one and proving another conjecture of Esperet, Kang and Thomassé. Complementing this result, we further obtain optimal bounds for this problem in the case of dense triangle-free graphs, and we also answer a question of Erdœs, Janson, Łuczak and Spencer.

Mathematics Subject Classification (2010)

05C35 

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Notes

Acknowledgements

We would like to thank the anonymous referees for their helpful comments and suggestions.

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag 2020

Authors and Affiliations

  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.ETH Institute for Theoretical StudiesETH ZurichZurichSwitzerland
  3. 3.Department of MathematicsETH ZurichZurichSwitzerland
  4. 4.School of Applied Mathematics and InformaticsHanoi University of Science and TechnologyHanoiVietnam

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