A rainbow Dirac theorem for loose Hamilton cycles in hypergraphs
Abstract
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.
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