Hypergraph

Hypergraph example: , .

A hypergraph is a generalization of a graph in which not only two vertices, but also any subsets of vertices can be connected with each edge.

From a mathematical point of view, a hypergraph is a pair where - non-empty set of objects of some nature, called the vertices of the hypergraph, and - family of non-empty (not necessarily different) subsets of the set called the edges of the hypergraph.

Hypergraphs are used, in particular, when modeling electrical circuits.

The transversal of a hypergraph is a set containing a non-empty intersection with each edge. Such a transversal will be minimal if none of its subsets are themselves a transversal of the hypergraph.

Literature [edit]

• V.A. Emelichev, O.I. Melnikov, V.I. Sarvanov, R.I. Tyszkiewicz Chapter XI: Hypergraphs // Lectures on graph theory. —M .: Science, 1990. — pp. 298–315. - 384 s. - ISBN 5-02-013992-0.
• I. A. Golovinskiy Methods for analyzing the topology of switching circuits of electrical networks // Electricity . - 2005. - № 3. - p. 10-18.
• V. A. Evstigneev, V. N. Kasyanov Explanatory Dictionary on Graph Theory. - Novosibirsk: Science, 1999.
• AA Zykov Hypergraphs // Uspekhi Matematicheskikh Nauk . - 1974. - № 6 (180).
• Kureichik V.M., Glushan V.M., Shcherbakov L.I. Combinatorial hardware models and algorithms in CAD. M .: Radio and communication, 1990. 216 p.