A survey on recent results on Balanced Graph and Hypergraph Designs

In this paper we recall some results on balanced type conditions for graph and hypergraph designs. The usual definition of balanced graph design (see [23]) is the following: a G-design is balanced if the number of blocks containing any vertex is constant. Later, other balanced type conditions have been introduced for graph designs and extended to hyper- graph designs. In the latter case the new notion of edge balanced has been introduced, being related to the number of times that a pair is contained in an edge of a block.