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arXiv · 2511.04953

The Rainbow Arborescence Problem on Cycles

Kristóf Bérczi·Tamás Király·Yutaro Yamaguchi·Yu Yokoi
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Abstract

The rainbow arborescence conjecture posits that if the arcs of a directed graph with $n$ vertices are colored by $n-1$ colors such that each color class forms a spanning arborescence, then there is a spanning arborescence that contains exactly one arc of every color. We prove that the conjecture is true if the underlying undirected graph is a cycle.

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Kristóf Bérczi, Tamás Király, Yutaro Yamaguchi, Yu Yokoi. 2025-12-09. The Rainbow Arborescence Problem on Cycles. https://arxiv.org/abs/2511.04953

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