Discussiones Mathematicae Graph Theory 27(3) (2007)
565582
doi: 10.7151/dmgt.1383
Stanisław Bylka and Jan Komar
Institute of Computer Science
Polish Academy of Sciences
21 Ordona street, 01237 Warsaw, Poland
email: bylka@ipipan.waw.pl
email: komjan@operamail.com

A necessary condition for the existence of such representation is the monotonicity of q on E i.e., if F ⊂ E then q(F) ≥ q(E). 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 multihypergraphs are formulated.
Keywords: intersection graph, intersection hypergraph.
2000 Mathematics Subject Classification: 05C62, 05C65.
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Received 13 February 2006
Revised 24 October 2007
Accepted 24 October 2007