Factorization operation on hypergraphs. (Russian) Zbl 0658.05058

Koganov, L. M.

Stud. Sci. Math. Hung. 19, 213-220 (1984).

For a hypergraph H, the intersection of all edges of H containing a given vertex \(\nu\) is called the minimal neighbourhood of \(\nu\). The factor- hypergraph Fact (H) of a hypergraph H has as vertex set the set of all minimal neighbourhoods of vertices of H, and a subset of the set of minimal neighbourhoods forms an edge of Fact (H) if and only if its union is an edge of H. It is shown that this factorization enables easy solving of some problems of hypergraph enumeration and Möbius functions.

MSC:

05C65	Hypergraphs
05C70	Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)

Keywords:

hypergraph; minimal neighbourhood; factorization; hypergraph enumeration; Möbius functions