Abstract
Given two graphs G = ( V G , E G ) and H = ( V H , E H ) , we ask under which conditions there is a relation R ⊆ V G × 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.
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