2025/01/13 by Amarja Kathapurkar, Patrick Morris, Kathapurkar, Amarja +3 · 1 citation
Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2501.07644
openalex publication_date 2025/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
A meta-conjecture of Coulson, Keevash, Perarnau and Yepremyan states that above the extremal threshold for a given spanning structure in a (hyper-)graph, one can find a rainbow version of that spanning structure in any suitably bounded colouring of the host (hyper-)graph. We solve one of the most pertinent outstanding cases of this conjecture, by showing that for any 1≤ j≤ k-1, if G is a k-uniform hypergraph above the j-degree threshold for a loose Hamilton cycle, then any globally bounded colouring of G contains a rainbow loose Hamilton cycle.