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Beispiele für die Verwendung von HYPERGRAPH in einem Satz

• In computational geometry, an undirected hypergraph may sometimes be called a range space and then the hyperedges are called ranges.
• A simple hypergraph is a hypergraph in which at most one hyperedge connects any pair of vertices and there are no hyperedges of size at most one.
• An opposite notion to a clutter is an abstract simplicial complex, where every subset of an edge is contained in the hypergraph; this is an order ideal in the poset of subsets of V.
• showed that the decision version of the betweenness problem (in which an algorithm must decide whether or not there exists a valid solution) is NP-complete in two ways, by a reduction from 3-satisfiability and also by a different reduction from hypergraph 2-coloring.
• Under the interpretation of a clean dessin as a map, an arbitrary dessin is a hypermap: that is, a drawing of a hypergraph in which the black points represent vertices and the white points represent hyperedges.
• This is the same method of cycle cutset using the definition of cutset for hypergraphs: a cycle hypercutset of a hypergraph is a set of edges (rather than vertices) that makes the hypergraph acyclic when all their vertices are removed.
• KaHyPar is a multilevel hypergraph partitioning framework providing direct k-way and recursive bisection based partitioning algorithms.
• Acyclicity of conjunctive queries is a structural property of queries that is defined with respect to the query's hypergraph: a conjunctive query is acyclic if and only if it has hypertree-width 1.
• The disjointness graph of a hypergraph H, denoted D(H), is the graph whose vertex set is the set of the hyperedges of H, with two vertices adjacent in D(H) when their corresponding hyperedges are disjoint in H.
• Some NP-complete problems for hypergraph degree sequences, CJ Colbourn, WL Kocay, DR Stinson – Discrete Applied Mathematics, 1986 – portal.
• If the hypergraph is required to be downward-closed (so it contains all hyperedges that are contained in some hyperedge) then the hypergraph is conformal precisely when it is a flag complex.
• Here, the treewidth can be the primal treewidth, dual treewidth, or incidence treewidth of the hypergraph associated to the SAT formula, whose vertices are the variables and where each clause is represented as a hyperedge.
• The condition on the closed neighborhood hypergraph also implies that a graph is dually chordal if and only if its square is chordal and its closed neighborhood hypergraph has the Helly property.
• of graph bipartiteness testing to 3-uniform hypergraphs: it asks whether the vertices of a hypergraph can be colored with two colors so that no hyperedge is monochromatic.
• With such hypergraph extension, multiple modalities of correspondences, including low-level appearance, saliency, coherent motion and high level features such as object regions, could be seamlessly incorporated in the hyperedge computation.
• A stronger definition of bipartiteness is: a hypergraph is called bipartite if its vertex set V can be partitioned into two sets, X and Y, such that each hyperedge contains exactly one element of X.
• Bipartiteness: The notion of a bipartiteness can be extended to hypergraphs in many ways (see bipartite hypergraph).
• A hypergraph in which some hyperedges are singletons (contain only one vertex) is obviously not 2-colorable; to avoid such trivial obstacles to 2-colorability, it is common to consider hypergraphs that are essentially 2-colorable, i.
• On the other hand, the hypergraph counting lemma estimates the number of hypergraphs of a given isomorphism class in some collections of the random-like parts.
• If the sets in the given family are interpreted as vertices in a hypergraph, with each element of the sets interpreted as a hyperedge incident to the sets containing that element, then the minimal set covers are the hyperedges of the transversal hypergraph.

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