## DIMACS TR: 93-35

## Entropy spiltting hypergraphs

### Author: Gabor Simonyi

**
ABSTRACT
**

Hypergraph entropy is an information theoretic functional on a
hypergraph with a probability distribution on its vertex set. It is
sub-additive with respect to the union of hypergraphs. In case of
simple graphs, exact additivity for the entropy of a graph and its
complement with respect to every probability distribution on the
vertex set gives a characterization of perfect graphs. Here we
investigate uniform hypergraphs with an analoguous behaviour of their
entropy. The main result is the characterization of 3-uniform
hypergraphs having this entropy splitting property. It is also shown
that for k>3 no non-trivial k-uniform hypergraph has this
property.

Paper available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1993/93-35.ps

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