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arXiv · 2505.01034

Ramsey with purple edges

Thomas Lesgourgues·Anita Liebenau·Nye Taylor
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Abstract

Motivated by a question of Angell, we investigate a variant of Ramsey numbers where some edges are coloured simultaneously red and blue, which we call purple. Specifically, we are interested in the largest number $g=g(n;s,t)$, for some $s$ and $t$ and $n<R(s,t)$, such that there exists a red/blue/purple colouring of $K_n$ with $g$ purple edges, with no red/purple copy of $K_s$ nor blue/purple copy of $K_t$. We determine $g$ asymptotically for a large family of parameters, exhibiting strong dependencies with Ramsey-Turán numbers.

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Thomas Lesgourgues, Anita Liebenau, Nye Taylor. 2025-05-20. Ramsey with purple edges. https://arxiv.org/abs/2505.01034

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