Relations Between Graphs
Jan Hubicka, J\"urgen Jost, Yangjing Long, Peter F. Stadler, Ling Yang

TL;DR
This paper explores conditions for relations between graphs that generate one graph's edges from another, generalizing homomorphisms and introducing concepts like R-cores and R-cocores, which are unique and computable efficiently.
Contribution
It introduces a generalized framework for graph relations, extending homomorphism concepts, and establishes the uniqueness and polynomial-time computability of R-cores and R-cocores.
Findings
R-cores and R-cocores are unique up to isomorphism
They can be computed in polynomial time
The framework generalizes existing graph homomorphism concepts
Abstract
Given two graphs G and H, we ask under which conditions there is a relation R that generates the edges of H given the structure of 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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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Topological and Geometric Data Analysis
