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arXiv · 2610.41971

The 3-Color 2-Chromatic Gallai-Ramsey Number for Complete Graphs

Mark Budden·Elijah DeJonge
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Abstract

For $1\le i\le j\le k$, let $gr^3_2(K_i, K_j, K_k)$ be the least $n\in \mathbb{N}$ such that every rainbow triangle-free $3$-coloring of $K_n$ (using red, blue, and green) contains a red/blue $K_i$, a red/green $K_j$, or a blue/green $K_k$. In this paper, we completely evaluate $gr^3_2(K_i, K_j, K_k)$ for all values of $i$, $j$, and $k$ in which $r(K_i,K_j)$ is known.

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Mark Budden, Elijah DeJonge. 2026-10-30. The 3-Color 2-Chromatic Gallai-Ramsey Number for Complete Graphs. https://arxiv.org/abs/2610.41971

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