On hypergraphs having evenly distributed subhypergraphs

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...

Morphological filtering on hypergraphs

The focus of this article is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of dual adjunctions between the vertex set and the hyper edge set of a hypergraph H , by defining a vertex-hyperedge correspondence. This allows us to recover the...

Subhypergraphs in Non-uniform Random Hypergraphs

In this paper we focus on the problem of finding (small) subhypergraphs in a (large) hypergraph. We use this problem to illustrate that reducing hypergraph problems to graph problems by working with the 2-section is not always a reasonable approach. We begin by defining a generalization of the binomial random graph model to hypergraphs and formalizing several definitions of subhypergraph. The b...

Minimal Decompositions of Hypergraphs into Mutually Isomorphic Subhypergraphs

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...