A sharp upper bound for the transversal number of k-uniform connected hypergraphs with given size

Zian Chen (), Bin Chen (), Zhongzheng Tang () and Zhuo Diao ()
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Zian Chen: Fuzhou University
Bin Chen: Hefei National Laboratory
Zhongzheng Tang: Beijing University of Posts and Telecommunications
Zhuo Diao: Central University of Finance and Economics

Journal of Combinatorial Optimization, 2023, vol. 45, issue 1, No 41, 21 pages

Abstract: Abstract For $$k\ge 2$$ k ≥ 2 , let H be a k-uniform connected hypergraph on n vertices and m edges. The transversal number $$\tau (H)$$ τ ( H ) is the minimum number of vertices that intersect every edge. We prove the following inequality: $$\tau (H)\le \frac{(k-1)m+1}{k}$$ τ ( H ) ≤ ( k - 1 ) m + 1 k . Furthermore, we characterize the extremal hypergraphs with equality holds. Based on the proofs, some combinatorial algorithms on the transversal number are designed.

Keywords: Transversal; k-uniform; Extremal hypergraph (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-022-00968-6

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