Abstract
Given two graphs G = (V-G,V- E-G) and H = (V-H, E-H), we ask under which conditions there is a relation R subset of V-G x V-H that generates the edges of H given the structure of the graph G. This construction can be seen as a form of multihomomorphism.
It generalizes surjective homomorphisms of graphs and naturally leads to notions of R-retractions, R-cores, and R-cocores of graphs. Both R-cores and R-cocores of graphs are unique up to isomorphism and can be computed in polynomial time.