On the complexity of deciding whether the distinguishing chromatic number of a graph is at most two

Elaine M. Eschen, Chính T. Hoàng, R. Sritharan, Lorna Stewart
2011 Discrete Mathematics  
In an article Cheng (2009) [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.
doi:10.1016/j.disc.2010.12.013 fatcat:5e2rkmi4v5axniblk5dyzehwsy