A Construction for Clique-Free Pseudorandom Graphs

Abstract

A construction of Alon and Krivelevich gives highly pseudorandom Kk-free graphs on n vertices with edge density equal to Θ(n−1=(k−2)). In this short note we improve their result by constructing an infinite family of highly pseudorandom Kk-free graphs with a higher edge density of Θ(n−1=(k−1)).

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Acknowledgments

We would like to thank David Conlon for his helpful remarks on an earlier draft of this paper. We would like to thank Akihiro Munemasa whose work together with the second author in [13, §6] on cospectral graphs inspired the current result. Finally, we would like to thank the referees for their careful reading and helpful comments.

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Correspondence to Anurag Bishnoi.

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Research supported in part by a Humboldt Research Fellowship for Postdoctoral Researchers and by Discovery Early Career Award of the Australian Research Council (No. DE190100666).

The author is supported by a postdoctoral fellowship of the Research Foundation — Flanders (FWO).

The author is supported by INDAM (Istituto Nazionale Di Alta Matemetica)

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Bishnoi, A., Ihringer, F. & Pepe, V. A Construction for Clique-Free Pseudorandom Graphs. Combinatorica 40, 307–314 (2020). https://doi.org/10.1007/s00493-020-4226-6

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Mathematics Subject Classification (2010)

  • 05D10
  • 51E20
  • 05E30