Minimum size transversals in uniform hypergraphs |
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Authors: | Zbigniew Lonc Karolina Warno |
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Institution: | Faculty of Mathematics and Information Science, Warsaw University of Technology, 00-661 Warsaw, Poland |
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Abstract: | A set of vertices in a hypergraph which meets all the edges is called a transversal. The transversal number τ(H) of a hypergraph H is the minimum cardinality of a transversal in H. A classical greedy algorithm for constructing a transversal of small size selects in each step a vertex which has the largest degree in the hypergraph formed by the edges not met yet. The analysis of this algorithm (by Chvátal and McDiarmid (1992) 3]) gave some upper bounds for τ(H) in a uniform hypergraph H with a given number of vertices and edges. We discuss a variation of this greedy algorithm. Analyzing this new algorithm, we obtain upper bounds for τ(H) which improve the bounds by Chvátal and McDiarmid. |
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Keywords: | Minimum-sized transversal Transversal number Uniform hypergraph Turan type problems |
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