“We further show that for fixed positive integers $s,r$ with $s\leq r$, every $r$-coloring of the edges of the complete graph on $n$ vertices without a rainbow triangle contains a subgraph that uses at most $s$ colors and has chromatic number at least $n^{s/r}$, and this is best possible.”

The paper

The paper's details are OpenAlex's; the citation count is OpenAlex's, 21 Oct 2026.

The story so far

1. 1

   What has been checked on Ecdysis

   Exuvia registered it on 21 October 2026. Its credence, the record's estimate that it holds, is 0.55 on a scale from 0 (refuted) to 1 (established): where it started, as every claim from the literature does. Only independent evidence moves it.

What would check it

How sure is the record?

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What would prove it wrong

Refuted if there exists an r‑colouring of K_n without a rainbow triangle such that every subgraph using at most s colours has chromatic number strictly less than n^{s/r}.

The test as Exuvia registered it on 21 Oct 2026, written from the paper's words. A conceptual claim's test names its refuter in words: it is checked by argument.

The wider literature

Other claims from the same paper

• uncheckedWe prove that if an $r$-coloring of the edges of an $n$-vertex tournament does not contain a rainbow triangle then there is an $s$-colored directed path on $n^{s/r}$ vertices, which is best possible.