Geodesic
The representation of multi-hypergraphs by set intersections
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 565-582.

Voir la notice de l'article provenant de la source Library of Science

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
Keywords: intersection graph, intersection hypergraph 
@article{DMGT_2007_27_3_a14,
     author = {Bylka, Stanis{\l}aw and Komar, Jan},
     title = {The representation of multi-hypergraphs by set intersections},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {565--582},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2007_27_3_a14/}
}
TY  - JOUR
AU  - Bylka, Stanisław
AU  - Komar, Jan
TI  - The representation of multi-hypergraphs by set intersections
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2007
SP  - 565
EP  - 582
VL  - 27
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2007_27_3_a14/
LA  - en
ID  - DMGT_2007_27_3_a14
ER  - 
%0 Journal Article
%A Bylka, Stanisław
%A Komar, Jan
%T The representation of multi-hypergraphs by set intersections
%J Discussiones Mathematicae. Graph Theory
%D 2007
%P 565-582
%V 27
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2007_27_3_a14/
%G en
%F DMGT_2007_27_3_a14
Bylka, Stanisław; Komar, Jan. The representation of multi-hypergraphs by set intersections. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 565-582. http://geodesic.mathdoc.fr/item/DMGT_2007_27_3_a14/

[1] C. Berge, Graphs and Hypergraphs (Amsterdam, 1973).

[2] J.C. Bermond and J.C. Meyer, Graphe représentatif des aretes d'un multigraphe, J. Math. Pures Appl. 52 (1973) 229-308.

[3] S. Bylka and J. Komar, Intersection properties of line graphs, Discrete Math. 164 (1997) 33-45, doi: 10.1016/S0012-365X(96)00041-6.

[4] P. Erdös, A. Goodman and L. Posa, The representation of graphs by set intersections, Canadian J. Math. 18 (1966) 106-112, doi: 10.4153/CJM-1966-014-3.

[5] F. Harary, Graph Theory (Addison-Wesley, 1969) 265-277.

[6] V. Grolmusz, Constructing set systems with prescribed intersection size, Journal of Algorithms 44 (2002) 321-337, doi: 10.1016/S0196-6774(02)00204-3.

[7] E.S. Marczewski, Sur deux properties des classes d'ensembles, Fund. Math. 33 (1945) 303-307.

[8] A. Marczyk, Properties of line multigraphs of hypergraphs, Ars Combinatoria 32 (1991) 269-278. Colloquia Mathematica Societatis Janos Bolyai, 18. Combinatorics, Keszthely (Hungary, 1976) 1185-1189.

[9] T.A. McKee and F.R. McMorris, Topics in Intersection Graph Theory, SIAM Monographs on Discrete Math. and Appl., 2 (SIAM Philadelphia, 1999).

[10] E. Prisner, Intersection multigraphs of uniform hypergraphs, Graphs and Combinatorics 14 (1998) 363-375.