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arXiv · 2508.14186

Rainbow Trees in Hypercubes

Nicholas Crawford·Maya Sankar·Carl Schildkraut·Sam Spiro
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Abstract

We prove that every proper edge-coloring of the $n$-dimensional hypercube $Q_n$ contains a rainbow copy of every tree $T$ on at most $n$ edges. This result is best possible, as $Q_n$ can be properly edge-colored using only $n$ colors while avoiding rainbow cycles.

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Nicholas Crawford, Maya Sankar, Carl Schildkraut, Sam Spiro. 2025-08-19. Rainbow Trees in Hypercubes. https://arxiv.org/abs/2508.14186

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