A relation on a hypergraph is a binary relation on the set consisting of the nodes and hyperedges together, and which satisfies a constraint involving the incidence structure of the hypergraph. These relations correspond to join-preserving mappings on the lattice of sub-hypergraphs. This paper studies the algebra of these relations, in particular the analogues of the familiar operations of complement and converse of relations. When generalizing from relations on a set to relations on a hypergraph we find that the Boolean algebra of relations is replaced by a weaker structure: a pair of isomorphic bi-Heyting algebras, one of which arises from the relations on the dual hypergraph. The paper also considers the representation of sub-hypergraphs as relations and applies the results obtained to mathematical morphology for hypergraphs. © 2012 Springer-Verlag.
CITATION STYLE
Stell, J. G. (2012). Relations on hypergraphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7560 LNCS, pp. 326–341). https://doi.org/10.1007/978-3-642-33314-9_22
Mendeley helps you to discover research relevant for your work.