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An edge-colored multigraph G is rainbow connected if every pair of vertices is joined by at least one rainbow path, i. e. , a path where no two edges are of the same color. In the context of multilayered networks we introduce the notion of multilayered random geometric graphs, from h 2 independent random geometric graphs G (n, r) on the unit square. We define an edge-coloring by coloring the edges according to the copy of G (n, r) they belong to and study the rainbow connectivity of the resulting edge-colored multigraph. We show that r (n) = (nn) ^h-1{2h} is a threshold of the radius for the property of being rainbow connected. This complements the known analogous results for the multilayerd graphs defined on the Erdos-R\' enyi random model.
Dı́az et al. (Wed,) studied this question.