# A Rainbow Connectivity Threshold for Random Graph Families

@inproceedings{Bradshaw2021ARC, title={A Rainbow Connectivity Threshold for Random Graph Families}, author={Peter Bradshaw and Bojan Mohar}, year={2021} }

Abstract. Given a family G of graphs on a common vertex set X, we say that G is rainbow connected if for every vertex pair u, v ∈ X, there exists a path from u to v that uses at most one edge from each graph in G. We consider the case that G contains s graphs, each sampled randomly from G(n, p), with n = |X| and p = c logn sn , where c > 1 is a constant. We show that when s is sufficiently large, G is a.a.s. rainbow connected, and when s is sufficiently small, G is a.a.s. not rainbow connected…

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