Abstract
We show that for any integer t≥2, every properly edge-coloured graph on n vertices with more than n1+o(1) edges contains a rainbow subdivision of Kt. Note that this bound on the number of edges is sharp up to the o(1) error term. This is a rainbow analogue of some classical results on clique subdivisions and extends some results on rainbow Turán numbers. Our method relies on the framework introduced by Sudakov and Tomon (2022) which we adapt to find robust expanders in the coloured setting.
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