Hamiltonian partition coloring

The hamiltonian coloring of a connected graph $G$ introduced by Chartrand et al cite {ch} is different from hamiltonian partition coloring. In this paper, we characterize graphs which has a hamiltonian partition. Also, we give example of graphs having prescribed chromatic numbers and hamiltonian partition numbers. We derive results connecting the hamiltonian chromatic number of $G_1 cup G_2$ and $G_1 + G_2$.