Rainbow Vertex-Connection Number

All the above parameters on rainbow connections involved edge-colorings of graphs. A natural idea is to introduce a similar parameter involving vertex-colorings of graphs. It is, as mentioned above, a vertex version of the rainbow connection number. Krivelevich and Yuster (J. Graph Theory 63(3):185–191, 2009) is the first to propose this new concept and proved a theorem analogous to the result of Theorem 3.1.10.