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Matching in hypergraphs information


In graph theory, a matching in a hypergraph is a set of hyperedges, in which every two hyperedges are disjoint. It is an extension of the notion of matching in a graph.[1]: 466–470  [2]

  1. ^ Lovász, László; Plummer, M. D. (1986), Matching Theory, Annals of Discrete Mathematics, vol. 29, North-Holland, ISBN 0-444-87916-1, MR 0859549
  2. ^ Berge, Claude (1973). Graphs and Hypergraphs. Amsterdam: North-Holland.

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Matching in hypergraphs

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3-dimensional matching – a special case of hypergraph matching to 3-uniform hypergraphs. Vertex cover in hypergraphs Bipartite hypergraph Rainbow matching in hypergraphs...

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Hypergraph

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hypergraphs, in particular: Matching in hypergraphs; Vertex cover in hypergraphs (also known as: transversal); Line graph of a hypergraph; Hypergraph...

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Maximum cardinality matching

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problem of finding a maximum-cardinality matching in hypergraphs is NP-complete even for 3-uniform hypergraphs. West, Douglas Brent (1999), Introduction...

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Perfect matching

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Envy-free matching Maximum-cardinality matching Perfect matching in high-degree hypergraphs Hall-type theorems for hypergraphs Alan Gibbons, Algorithmic Graph...

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Rainbow matching

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fractional matchings. In contrast, the case of rainbow integral matchings in r-uniform hypergraphs is much less understood. The number of required matchings for...

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Bipartite graph

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corresponding hypergraphs. As a special case of this correspondence between bipartite graphs and hypergraphs, any multigraph (a graph in which there may...

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Balanced hypergraph

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maximum matching. The Kőnig-Egervary theorem says that all bipartite graphs have the Konig property. The balanced hypergraphs are exactly the hypergraphs H...

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Vertex cover in hypergraphs

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optimization. Matching in hypergraphs – discusses also the duality between vertex-cover and matching. Lovász, László; Plummer, M. D. (1986), Matching Theory...

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Bipartite hypergraph

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In graph theory, the term bipartite hypergraph describes several related classes of hypergraphs, all of which are natural generalizations of a bipartite...

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Line graph of a hypergraph

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In graph theory, particularly in the theory of hypergraphs, the line graph of a hypergraph H, denoted L(H), is the graph whose vertex set is the set of...

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Truncated projective plane

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hypergraphs". Ars Combinatorica. Abu-Khazneh, Ahmad; Barát, János; Pokrovskiy, Alexey; Szabó, Tibor (2018-07-12). "A family of extremal hypergraphs for...

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Clique complex

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flag complexes, Whitney complexes and conformal hypergraphs are closely related mathematical objects in graph theory and geometric topology that each describe...

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Property B

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Matching Theory, Annals of Discrete Mathematics, vol. 29, North-Holland, ISBN 0-444-87916-1, MR 0859549 Beck, J. (1978), "On 3-chromatic hypergraphs"...

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Fractional matching

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Füredi, Zoltán (1981-06-01). "Maximum degree and fractional matchings in uniform hypergraphs". Combinatorica. 1 (2): 155–162. doi:10.1007/BF02579271. ISSN 1439-6912...

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List of graph theory topics

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algorithm Strongly connected component Vertex cover problem See list of network theory topics Helly family Intersection (Line) Graphs of hypergraphs...

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Width of a hypergraph

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all H: w(H) ≥ mw(H). The width of a hypergraph is used in Hall-type theorems for hypergraphs. Let H be the hypergraph with vertex set V = {A,B; a,b} and...

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Helly family

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into a space with Helly dimension 1. A hypergraph is equivalent to a set-family. In hypergraphs terms, a hypergraph H = (V, E) has the Helly property if...

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Graph isomorphism problem

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regular graphs was done by Spielman (1996). For hypergraphs of bounded rank, a subexponential upper bound matching the case of graphs was obtained by Babai &...

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Vertex cover

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program is the maximum matching problem. Vertex cover problems have been generalized to hypergraphs, see Vertex cover in hypergraphs. Formally, a vertex...

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Packing in a hypergraph

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of edges in each subset share any vertex. There are two famous algorithms to achieve asymptotically optimal packing in k-uniform hypergraphs. One of them...

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Independence complex

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S2CID 38277360. Meshulam, Roy (2001-01-01). "The Clique Complex and Hypergraph Matching". Combinatorica. 21 (1): 89–94. doi:10.1007/s004930170006. ISSN 1439-6912...

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