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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 nn vertices are colored by n1n-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.

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

R2 v1 2026-07-01T07:25:36.756Z