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The Sub-Exponential Transition for the Chromatic Generalized Ramsey Numbers

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Abstract

A simple graph-product type construction shows that for all natural numbers r≥q, there exists an edge-coloring of the complete graph on 2r vertices using r colors where the graph consisting of the union of any q color classes has chromatic number 2q. We show that for each fixed natural number q, if there exists an edge-coloring of the complete graph on n vertices using r colors where the graph consisting of the union of any q color classes has chromatic number at most 2q − 1, then n must be sub-exponential in r. This answers a question of Conlon, Fox, Lee, and Sudakov.

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Authors and Affiliations

  1. Department of Mathematics, MIT, Cambridge, MA, 02139-4307, USA

    Choongbum Lee & Brandon Tran

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  1. Choongbum Lee
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  2. Brandon Tran
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Correspondence to Choongbum Lee.

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Research supported by NSF Grant DMS-1362326.

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Lee, C., Tran, B. The Sub-Exponential Transition for the Chromatic Generalized Ramsey Numbers. Combinatorica 39, 355–376 (2019). https://doi.org/10.1007/s00493-017-3474-6

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  • DOI: https://doi.org/10.1007/s00493-017-3474-6

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