  An (m,n)-colored mixed graph, or simply, an (m,n)-graph is a graph having m
different types of arcs and n different types of edges. A homomorphism of an
(m,n)-graph G to another (m,n)-graph H is a vertex mapping that preserves
adjacency, the type thereto and the direction. A subset R of the set of
vertices of G that always maps distinct vertices in itself to distinct image
vertices under any homomorphism is called an (m,n)-relative clique of G. The
maximum cardinality of an (m,n)-relative clique of a graph is called the
(m,n)-relative clique number of the graph. In this article, we explore the
(m,n)-relative clique numbers for various families of graphs.
