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Dense Induced Bipartite Subgraphs in Triangle-Free Graphs

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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.

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Acknowledgements

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

Author information

Authors and Affiliations

  1. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    Matthew Kwan

  2. ETH Institute for Theoretical Studies, ETH Zurich, Zurich, Switzerland

    Shoham Letzter

  3. Department of Mathematics, ETH Zurich, Zurich, Switzerland

    Benny Sudakov

  4. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam

    Tuan Tran

Authors
  1. Matthew Kwan
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  2. Shoham Letzter
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  3. Benny Sudakov
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  4. Tuan Tran
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Corresponding author

Correspondence to Shoham Letzter.

Additional information

Research supported in part by SNSF project 178493.

Research supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zurich Foundation.

Research supported in part by SNSF grant 200021-175573.

Research supported by the Alexander von Humboldt Foundation.

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Kwan, M., Letzter, S., Sudakov, B. et al. Dense Induced Bipartite Subgraphs in Triangle-Free Graphs. Combinatorica 40, 283–305 (2020). https://doi.org/10.1007/s00493-019-4086-0

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  • DOI: https://doi.org/10.1007/s00493-019-4086-0

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