The rainbow 2-connectivity of Cartesian products of 2-connected graphs and paths - Bety Hayat Susanti; A.N.M. Salman; Rinovia Simanjuntak (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2020)
An edge-colored graph G is rainbow k-connected, if there are k-internally disjoint rainbow paths connecting every pair of vertices of G. The rainbow k-connection number of G, denoted by rck(G), is the minimum number of colors needed for which there exists a rainbow k-connected coloring for G. In this paper, we are able to find sharp lower and upper bounds for the rainbow 2-connection number of Cartesian products of arbitrary 2-connected graphs and paths. We also determine the rainbow 2-connection number of the Cartesian products of some graphs, i.e. complete graphs, fans, wheels, and cycles, with paths.