9 8
14th WORKSHOP
‘3in1’ GRAPHS 2005
Dobczyce, November 10-12, 2005
THE REPRESENTATION OF MULTI-HYPERGRAPHS BY SET INTERSECTIONS
StanisÃlaw Bylka and Jan Komar Institute of Computer Science
Polish Academy of Sciences 21 Ordona street, 01–237 Warsaw, Poland
e-mail: bylka@ipipan.waw.pl e-mail: komjan@operamail.com
Abstract
This paper deals with weighted set systems (V, E, q), where V is a set of indices, E ⊂ 2
Vand the weight q is a nonnegative integer function on E. 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, E, q) is defined to be an indexed family R = (R
v)
v∈Vof subsets of a set S such that
¯ ¯
¯ \
v∈E