Maximizing Vertex-Disjoint and Edge-Disjoint Clique Packings in Bounded Degree Graphs

The authors study the problem of finding a maximum-cardinality set of r-cliques in an undirected graph of fixed maximum degree Δ, subject to the cliques being either vertex disjoint or edge disjoint. They provide a complete complexity classification for both the vertex-disjoint and edge-disjoint variants.