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Let \(H=(V,E)\) be a hypergraph with n vertices and m edges. \(A\subseteq E\) is an eliminating edge feedback set of H if \(H/\!\!/A\) has no cycle and \(D_c'(H)\) denote the minimum cardinality of an eliminating edge feedback set of H. In this paper, we prove (i) for any hypergraph H, \(D_c'(H)\le n/2\) . (ii) for any hypergraph H with maximum degree \(\varDelta \le 2\) and girth \(k\ge 4\) , \(D_c'(H)\le \frac{n}{4}\) . (iii) for any hypergraph H with maximum degree \(\varDelta \le 3\) and girth \(k\ge 3\) , \(D_c'(H)\le \frac{n}{3}\) . Based on the proofs, some combinatorial algorithms on the eliminating edge feedback number are designed.

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Some Combinatorial Algorithms on the Eliminating Edge Feedback Number of Hypergraphs

  • 会议论文

  • 发表日期：

    2026年

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  • Zhongzheng Tang,
  • Haoyang Zou,
  • Zhuo Diao

摘要

Let \(H=(V,E)\) be a hypergraph with n vertices and m edges. \(A\subseteq E\) is an eliminating edge feedback set of H if \(H/\!\!/A\) has no cycle and \(D_c'(H)\) denote the minimum cardinality of an eliminating edge feedback set of H. In this paper, we prove (i) for any hypergraph H, \(D_c'(H)\le n/2\) . (ii) for any hypergraph H with maximum degree \(\varDelta \le 2\) and girth \(k\ge 4\) , \(D_c'(H)\le \frac{n}{4}\) . (iii) for any hypergraph H with maximum degree \(\varDelta \le 3\) and girth \(k\ge 3\) , \(D_c'(H)\le \frac{n}{3}\) . Based on the proofs, some combinatorial algorithms on the eliminating edge feedback number are designed.