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On the anti-Ramsey threshold

2025/01/06 by Eden Kuperwasser, Kuperwasser, Eden
Mathematics · #05C80 #05D10 #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2501.03439

openalex publication_date 2025/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We say that a graph G is anti-Ramsey for a graph H if any proper edge-colouring of G yields a rainbow copy of H, i.e. a copy of H whose edges all receive different colours. In this work we determine the threshold at which the binomial random graph becomes anti-Ramsey for any fixed graph H, given that H is sufficiently dense. Our proof employs a graph decomposition lemma in the style of the Nine Dragon Tree theorem that may be of independent interest.

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