The Rainbow Arborescence Problem on Cycles
Combinatorics
2025-12-10 v2 Discrete Mathematics
Abstract
The rainbow arborescence conjecture posits that if the arcs of a directed graph with vertices are colored by 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.
Keywords
Cite
@article{arxiv.2511.04953,
title = {The Rainbow Arborescence Problem on Cycles},
author = {Kristóf Bérczi and Tamás Király and Yutaro Yamaguchi and Yu Yokoi},
journal= {arXiv preprint arXiv:2511.04953},
year = {2025}
}
Comments
This work has been merged with arXiv:2412.15457