The upper chromatic number χ(H) of a hypergraph H is the maximum number of colors in a coloring avoiding a polychromatic edge. The stability number α(H) of a hypergraph H is the cardinality of the largest set of vertices of H which does not contain an edge. A hypergraph is k-uniform if the sizes of all its edges are k. A hypergraph H is co-perfect if χ(H ′) = α(H ′) for each induced subhypergra...

Some classical models of clustering (hierarchies, pyramids, . . . ) are related to interval hypergraphs. In this paper we study clustering models related to hypertrees which are an extension of interval hypergraphs. We first prove that a hypertree can be characterized by an order on its vertices, this order allowing to find one of its underlying vertex trees. We then focus on clustering models ...

In this paper, we propose a novel hypergraph based method (called HF) to fit and segment multi-structural data. The proposed HF formulates the geometric model fitting problem as a hypergraph partition problem based on a novel hypergraph model. In the hypergraph model, vertices represent data points and hyperedges denote model hypotheses. The hypergraph, with large and “data-determined” degrees ...

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...

Four consequence operators based on hypergraph satisfiability are defined. Their properties are explored and interconnections are displayed. Finally their relation to the case of the Classical Propositional Calculus is shown. 1. Preliminaries. Let us recall some definitions and facts which can also be found in Cowen [1,2] and Kolany [3]. A hypergraph is a structure G = (V, E), where V is a set ...

Basic definitions. For X a finite set of vertices, a hypergraph H on X is a family of subsets (called edges) of X. In a directed hypergraph H, every set h E H contains a distinguished element called the head of h (a set h may appear more than once in H but with different heads). A hypergraph H’ is a subhypergraph of H iff H’ c H. A directed hypergraph H is an arborescence iff (i) H is empty, or...