Rainbow meta-conjecture above extremal thresholds

Establish that, for every spanning structure in a graph or hypergraph, exceeding the extremal minimum-degree threshold guarantees a rainbow copy of that spanning structure in every suitably bounded edge-colouring of the host graph or hypergraph.

Background

The paper situates its main theorem within a broader meta-conjecture attributed to Coulson, Keevash, Perarnau and Yepremyan. The conjecture predicts that the robustness of Dirac-type minimum-degree thresholds extends to rainbow spanning structures under appropriate global or local bounds on colour classes.

The present work verifies this phenomenon for loose Hamilton cycles in hypergraphs, but the general meta-conjecture remains unresolved for many other spanning structures and Hamilton-cycle types.