%0 Journal Article %T On the complexity of deciding whether the distinguishing chromatic number of a graph is at most two %A Elaine M. Eschen %A Chinh T. Hoang %A R. Sritharan %A Lorna Stewart %J Computer Science %D 2009 %I arXiv %X In an article [3] published recently in this journal, it was shown that when k >= 3, the problem of deciding whether the distinguishing chromatic number of a graph is at most k is NP-hard. We consider the problem when k = 2. In regards to the issue of solvability in polynomial time, we show that the problem is at least as hard as graph automorphism but no harder than graph isomorphism. %U http://arxiv.org/abs/0907.0691v1