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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Definable Kőnig theorems
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by Matt Bowen and Felix Weilacher
Proc. Amer. Math. Soc. 151 (2023), 4991-4996
DOI: https://doi.org/10.1090/proc/16355
Published electronically: July 28, 2023

Abstract:

Let $X$ be a Polish space with Borel probability measure $\mu ,$ and let $G$ be a Borel graph on $X$ with no odd cycles and maximum degree $\Delta (G).$ We show that the Baire measurable edge chromatic number of $G$ is at most $\Delta (G)+1$, and if $G$ is $\mu$-hyperfinite then the $\mu$-measurable edge chromatic number obeys the same bound. More generally, we show that $G$ has Borel edge chromatic number at most $\Delta (G)$ plus its asymptotic separation index.
References
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Bibliographic Information
  • Matt Bowen
  • Affiliation: Department of Mathematics and Statistics, McGill University, Burneside Hall 1020, Montreal, Quebec H3A 0B9, Canada
  • MR Author ID: 1389674
  • Email: matthew.bowen2@mail.mcgill.ca
  • Felix Weilacher
  • Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Wean Hall 6113, Pittsburgh, Pennsylvania 15213
  • MR Author ID: 1394099
  • Email: fweilach@andrew.cmu.edu
  • Received by editor(s): January 10, 2022
  • Received by editor(s) in revised form: September 17, 2022
  • Published electronically: July 28, 2023
  • Additional Notes: The second author was partially supported by the ARCS foundation, Pittsburgh chapter.
  • Communicated by: Vera Fischer
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 4991-4996
  • MSC (2020): Primary 03E15, 05C70
  • DOI: https://doi.org/10.1090/proc/16355