Abstract:
A path of G is a rainbow path if all of its vertices have distinct colors or its internal vertices have distinct colors. In other words,the endpoints have the same colors. If for every pair u,v of distinct vertices, G contains a revised rainbow vertex u-v path, then G is revised rainbow vertex-connected. The minimum number k of G that results in a revised rainbow vertex-connected graph is called the revised rainbow vertex-connection number of G, denoted by rvc*(G).It is proved that rvc*(G)≤n2+1 for 2-connected graphs.
