symmetrical hypergraph - definição. O que é symmetrical hypergraph. Significado, conceito
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O que (quem) é symmetrical hypergraph - definição

2-colorable hypergraph; 2-colourable hypergraph

Hypergraph         
  • This [[circuit diagram]] can be interpreted as a drawing of a hypergraph in which four vertices (depicted as white rectangles and disks) are connected by three hyperedges drawn as trees.
  • An example of a directed hypergraph, with
<math>X = \{1, 2, 3, 4, 5, 6\}</math> and
<math>E = \{a_1, a_2, a_3, a_4, a_5\} = </math>
<math>\{(\{1\}, \{2\}),</math>
<math>(\{2\}, \{3\}),</math>
<math>(\{3\}, \{1\}),</math>
<math>(\{2, 3\}, \{4, 5\}),</math>
<math>(\{3, 5\}, \{6\})\}</math>.
  • url-status=live}}</ref> Edges are vertical lines connecting vertices. V7 is an isolated vertex. Vertices are aligned to the left. The legend on the right shows the names of the edges.
  • An order-4 Venn diagram, which can be interpreted as a subdivision drawing of a hypergraph with 15 vertices (the 15 colored regions) and 4 hyperedges (the 4 ellipses).
GENERALIZATION OF A GRAPH IN WHICH GENERALIZED EDGES MAY CONNECT MORE THAN TWO NODES
Host graph; Gaifman graph; Primal graph (hypergraphs); Dual hypergraph; Hypergraphs; Hypergraph acyclicity; Alpha-acyclic; Hypergraph (mathematics); Directed hypergraph; Hyper-graph
In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two vertices.
Bipartite hypergraph         
In graph theory, the term bipartite hypergraph describes several related classes of hypergraphs, all of which are natural generalizations of a bipartite graph.
Symmetric hypergraph theorem         
The Symmetric hypergraph theorem is a theorem in combinatorics that puts an upper bound on the chromatic number of a graph (or hypergraph in general). The original reference for this paper is unknown at the moment, and has been called folklore.

Wikipédia

Property B

In mathematics, Property B is a certain set theoretic property. Formally, given a finite set X, a collection C of subsets of X has Property B if we can partition X into two disjoint subsets Y and Z such that every set in C meets both Y and Z.

The property gets its name from mathematician Felix Bernstein, who first introduced the property in 1908.

Property B is equivalent to 2-coloring the hypergraph described by the collection C. A hypergraph with property B is also called 2-colorable.: 468  Sometimes it is also called bipartite, by analogy to the bipartite graphs. Property B is often studied for uniform hypergraphs (set systems in which all subsets of the system have the same cardinality) but it has also been considered in the non-uniform case.

The problem of checking whether a collection C has Property B is called the set splitting problem.