Transversals and domination in uniform hypergraphs
نویسندگان
چکیده
منابع مشابه
Total Transversals and Total Domination in Uniform Hypergraphs
In 2012, the first three authors established a relationship between the transversal number and the domination number of uniform hypergraphs. In this paper, we establish a relationship between the total transversal number and the total domination number of uniform hypergraphs. We prove tight asymptotic upper bounds on the total transversal number in terms of the number of vertices, the number of...
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Let H be a 4-uniform hypergraph on n vertices. The transversal number τ(H) of H is the minimum number of vertices that intersect every edge. The result in [J. Combin. Theory Ser. B 50 (1990), 129–133] by Lai and Chang implies that τ(H) 6 7n/18 when H is 3-regular. The main result in [Combinatorica 27 (2007), 473–487] by Thomassé and Yeo implies an improved bound of τ(H) 6 8n/21. We provide a fu...
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The main result of this paper is that every 4-uniform hypergraph on n vertices and m edges has a transversal with no more than (5n+4m)/21 vertices. In the particular case n = m, the transversal has at most 3n/7 vertices, and this bound is sharp in the complement of the Fano plane. Chvátal and McDiarmid [5] proved that every 3-uniform hypergraph with n vertices and edges has a transversal of siz...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2012
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2011.08.002