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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0023-9,
author = {Michael Henning and Christian L\"owenstein},
title = {Hypergraphs with large transversal number and with edge sizes at least four},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {1133-1140},
zbl = {1242.05192},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0023-9}
}
Michael Henning; Christian Löwenstein. Hypergraphs with large transversal number and with edge sizes at least four. Open Mathematics, Tome 10 (2012) pp. 1133-1140. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0023-9/
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