We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Given two graphs G=(V_G,E_G) and H=(V_H,E_H), we ask under which conditions there is a relation that generates the edges of H given the structure of G. This construction generalizes full homomorphisms of graphs and naturally leads to generalized notions of retractions, cores, and co-cores of graphs.