A partition of the vertices of a graph G into k pairwise disjoint sets V 1 ,...,V k is called an (r 1 ,...,r k )-subcoloring if the subgraph G i of G induced by V i ,1=<i=<k, consists of disjoint complete subgraphs, each of which has cardinality no more than r i . Due to Erdos and Albertson et al., independently, every cubic (i.e., 3-regular) graph has a (2,2)-subcoloring. Albertson et al. then asked for cubic graphs having (1,2)-subcolorings. We point out in this paper that this question is algorithmically difficult by showing that recognizing (1,2)-subcolorable cubic graphs is NP-complete, even when restricted to triangle-free planar graphs.