In graph theory, a subcoloring is an assignment of colors to a graph's vertices such that each color class induces a vertex disjoint union of cliques.
A subchromatic number χS(G) of a graph G is the least number of colors needed in any subcoloring of G.
Subcoloring and subchromatic number were introduced by Albertson et al. (1989).
Every proper coloring and cocoloring of a graph are also subcolorings, so the subchromatic number of any graph is at most equal to the cochromatic number, which is at most equal to the chromatic number.
Subcoloring is as difficult to solve exactly as coloring, in the sense that (like coloring) it is NP-complete. More specifically, the problem of determining whether a triangle-free planar graph with maximum degree 4 has subchromatic number at most 2 is NP-complete (Gimbel & Hartman 2003).