Entropy Splitting Hypergraphs

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 fork⩾4 no non-trivialk-uniform hypergraph has this property.