Minimal Decompositions of Hypergraphs into Mutually Isomorphic Subhypergraphs

Minimal Decompositions of Hypergraphs into Mutually Isomorphic Subhypergraphs

Relations on Hypergraphs

A relation on a hypergraph is a binary relation on the set consisting of the nodes and hyperedges together, and which satisfies a constraint involving the incidence structure of the hypergraph. These relations correspond to join-preserving mappings on the lattice of subhypergraphs. This paper studies the algebra of these relations, in particular the analogues of the familiar operations of compl...

On hypergraphs having evenly distributed subhypergraphs

Chung, F.R.K. and R.L. Graham, On hypergraphs having evenly distributed subhypergraphs, Discrete Mathematics 111 (1993) 125-129.

On the upper chromatic number of a hypergraph

We introduce the notion of a of a hypergraph, which is a subset of vertices to be colored so that at least two vertices are of the same color. Hypergraphs with both and are called mixed hypergraphs. The maximal number of colors for which there exists a mixed hypergraph coloring using all the colors is called the upper chromatic number of a hypergraph H and is denoted by X(H). An algorithm for c...

Equicovering Subgraphs of Graphs and Hypergraphs

As a variation on the t-Equal Union Property (t-EUP) introduced by Lindström, we introduce the t-Equal Valence Property (t-EVP) for hypergraphs: a hypergraph satisfies the t-EVP if there are t pairwise edge-disjoint subhypergraphs such that for each vertex v, the degree of v in all t subhypergraphs is the same. In the t-EUP, the subhypergraphs just have the same sets of vertices with positive d...