On graphs with equal chromatic transversal domination and connected domination numbers

Let G - (V, E) be a graph with chromatic number chi(G). A dominating set D of G is called a chromatic transversal dominating set (ctd-set) if D intersects every color class of every chi-partition of G. The minimum cardinality of a ctd-set of G is called the chromatic transversal domination number of G and is denoted by gamma ct(G). In this paper we characterize the class of trees, unicyclic graphs and cubic graphs for which the chromatic transversal domination number is equal to the connected domination number