Rainbow connectivity of multilayered random geometric graphs

Abstract

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) = lnn nh-1 1/2h , is a threshold of the radius for the property of being rainbow connected. This complements the known analogous results for the multilayered graphs defined on the Erdos–Rényi random model.

Peer Reviewed

Postprint (published version)