Hypergraphs with large transversal number and with edge sizes at least four

• Autorzy: Michael Henning , Christian Löwenstein
• Języki publikacji: EN

Abstrakty

EN

Let H be a hypergraph on n vertices and m edges with all edges of size at least four. The transversal number τ(H) of H is the minimum number of vertices that intersect every edge. Lai and Chang [An upper bound for the transversal numbers of 4-uniform hypergraphs, J. Combin. Theory Ser. B, 1990, 50(1), 129–133] proved that τ(H) ≤ 2(n+m)/9, while Chvátal and McDiarmid [Small transversals in hypergraphs, Combinatorica, 1992, 12(1), 19–26] proved that τ(H) ≤ (n + 2m)/6. In this paper, we characterize the connected hypergraphs that achieve equality in the Lai-Chang bound and in the Chvátal-McDiarmid bound.

Słowa kluczowe

EN

Transversal; 4-uniform hypergraph

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques
• 05C65: Hypergraphs

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 3
• Strony: 1133-1140

Daty

wydano

2012-06-01

online

2012-03-24

Twórcy

autor

Michael Henning

• University of Johannesburg

autor

Christian Löwenstein

• University of Johannesburg

Bibliografia

• [1] Chvátal V., McDiarmid C., Small transversals in hypergraphs, Combinatorica, 1992, 12(1), 19–26 http://dx.doi.org/10.1007/BF01191201
• [2] Henning M.A., Yeo A., Hypergraphs with large transversal number and with edge sizes at least 3, J. Graph Theory, 2008, 59(4), 326–348
• [3] Lai F.C., Chang G.J., An upper bound for the transversal numbers of 4-uniform hypergraphs, J. Combin. Theory Ser. B, 1990, 50(1), 129–133 http://dx.doi.org/10.1016/0095-8956(90)90101-5
• [4] Thomassé S., Yeo A., Total domination of graphs and small transversals of hypergraphs, Combinatorica, 2007, 27(4), 473–487 http://dx.doi.org/10.1007/s00493-007-2020-3
• [5] Tuza Zs., Covering all cliques of a graph, Discrete Math., 1990, 86(1–3), 117–126 http://dx.doi.org/10.1016/0012-365X(90)90354-K
• [6] Yeo A., private communication

Identyfikatory

DOI

10.2478/s11533-012-0023-9