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arXiv · 1507.04792

A sub-exponential transition of the chromatic generalized Ramsey numbers

Choongbum Lee·Brandon Tran
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Abstract

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

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Choongbum Lee, Brandon Tran. 2015-07-16. A sub-exponential transition of the chromatic generalized Ramsey numbers. https://arxiv.org/abs/1507.04792

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