Rainbow connection for some families of hypergraphs

An edge-coloured path in a graph is rainbow if its edges have distinct colours. The rainbow connection number   of a connected graph GG, denoted by rc(G)rc(G), is the minimum number of colours required to colour the edges of GG so that any two vertices of GG are connected by a rainbow path. The function rc(G)rc(G) was first introduced by Chartrand et al. (2008), and has since attracted considerable interest. In this paper, we introduce two extensions of the rainbow connection number to hypergraphs. We study these two extensions of the rainbow connection number in minimally connected hypergraphs, hypergraph cycles and complete multipartite hypergraphs.