- An anticoloring of a graph is a partial coloring of the vertices in which no two adjacent vertices are colored in distinct colors. In the basic anticoloring problem, we are given a graph G and positive integers B 1 , ? , B k , and have to determine whether there exists an anticoloring of G such that B j vertices are colored in color j , 1 ? j ? k . This problem is known to be NP-complete, even for two colors.We deal with the anticoloring problem on the rook's graph. In general, we are able to provide sub-linear algorithms. In some particular cases, we give an explicit formula for the optimal solution.