- Tytuł:
- The representation of multi-hypergraphs by set intersections
- Autorzy:
-
Bylka, Stanisław
Komar, Jan - Powiązania:
- https://bibliotekanauki.pl/articles/743464.pdf
- Data publikacji:
- 2007
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
intersection graph
intersection hypergraph - Opis:
-
This paper deals with weighted set systems (V,,q), where V is a set of indices, $ ⊂ 2^V$ and the weight q is a nonnegative integer function on . The basic idea of the paper is to apply weighted set systems to formulate restrictions on intersections. It is of interest to know whether a weighted set system can be represented by set intersections. An intersection representation of (V,,q) is defined to be an indexed family $R = (R_v)_{v∈ V}$ of subsets of a set S such that
$|⋂_{v∈ E} R_v| = q(E)$ for each E ∈ .
A necessary condition for the existence of such representation is the monotonicity of q on i.e., if F ⊂ then q(F) ≥ q(). Some sufficient conditions for weighted set systems representable by set intersections are given. Appropriate existence theorems are proved by construction of the solutions. The notion of intersection multigraphs to intersection multi- hypergraphs - hypergraphs with multiple edges, is generalized. Some conditions for intersection multi-hypergraphs are formulated. - Źródło:
-
Discussiones Mathematicae Graph Theory; 2007, 27, 3; 565-582
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł