an:04075122
Zbl 0658.05058
Koganov, L. M.
Factorization operation on hypergraphs
RU
Stud. Sci. Math. Hung. 19, 213-220 (1984).
00147479
1984
j
05C65 05C70
hypergraph; minimal neighbourhood; factorization; hypergraph enumeration; M??bius functions
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 M??bius functions.