Algorithms for maximum k-colorings and k-coverings of transitive graphs

Consider a graph G and a positive integer k. The maximum k-coloring problem is to color a maximum number of vertices using k colors, such that no two adjacent vertices have the same color. The maximum k-covering problem is to find k disjoint cliques covering a maximum number of vertices. The present paper contains polynomial time algorithms for finding maximum k-colorings and maximum k-coverings of transitive graphs.