Hamiltonian Partition Coloring
Mudartha Kulrekha, R. Sundareswaran, V. Swaminathan · International Journal of Mathematics and Soft Computing · 2011
Coloring of vertices/edges in graphs has been studied by many authors and various types of coloring were also introduced. A proper coloring is a partition of the vertex set into independent sets based on the properties of the chromatic partition ( which is a partition of minimum cardinality into independent sets). Other notions like achromatic coloring, b-coloring etc, have been introduced. A proper coloring P of G is called a hamiltonian partition coloring if P ( G ) is hamiltonian. The maximum cardinality of a hamiltonian partition coloring of G is called the hamiltonian partition achromatic number of G and is denoted by h ( G ). The hamiltonian coloring of a connected graph G introduced by Chartrand et al [1] 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 [ G 2 and G 1 + G 2 .