Rainbow Trees in Hypercubes
Crawford, Nicholas, Maya Sankar, Carl Schildkraut, Sam Spiro · arXiv (Cornell University) · 2025
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.