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Journal of the American Mathematical Society

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Non-concentration of the chromatic number of a random graph


Author: Annika Heckel
Journal: J. Amer. Math. Soc. 34 (2021), 245-260
MSC (2020): Primary 05C15, 05C80
DOI: https://doi.org/10.1090/jams/957
Published electronically: December 3, 2020
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Abstract: We show that the chromatic number of $ G_{n, \frac {1}{2}}$ is not concentrated on fewer than $ n^{\frac {1}{4}-\epsilon }$ consecutive values. This addresses a longstanding question raised by Erdős and several other authors.


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Additional Information

Annika Heckel
Affiliation: Mathematisches Institut der Universität München, Theresienstr. 39, 80333 München, Germany
Email: heckel@math.lmu.de

DOI: https://doi.org/10.1090/jams/957
Received by editor(s): June 27, 2019
Received by editor(s) in revised form: January 17, 2020, and April 1, 2020
Published electronically: December 3, 2020
Additional Notes: This research was funded by ERC Grants 676632-RanDM and 772606-PTRCSP.
Article copyright: © Copyright 2020 American Mathematical Society