Rainbow Connection of Random Regular Graphs Andrzej Dudek Alan Frieze Charalampos E. Tsourakakis 10.1184/R1/6479219.v1 https://kilthub.cmu.edu/articles/journal_contribution/Rainbow_Connection_of_Random_Regular_Graphs/6479219 <p>An edge colored graph G is rainbow edge connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection of a connected graph G, denoted by rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. <br>In this work we study the rainbow connection of the random r-regular graph G=G(n,r) of ordern, where r≥4 is a constant. We prove that with probability tending to one as n goes to infinity the rainbow connection of G satisfies rc(G)=O(logn), which is best possible up to a hidden constant.</p> 2013-11-11 00:00:00 Mathematical Sciences