Characterizing 3-uniform linear extremal hypergraphs on feedback vertex number

Zhongzheng Tang (), Yucong Tang () and Zhuo Diao ()
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Zhongzheng Tang: School of Science, Beijing University of Posts and Telecommunications
Yucong Tang: Nanjing University of Aeronautics and Astronautics
Zhuo Diao: School of Statistics and Mathematics, Central University of Finance and Economics

Journal of Combinatorial Optimization, 2022, vol. 44, issue 5, No 7, 3310-3330

Abstract: Abstract Let $$H=(V,E)$$ H = ( V , E ) be a hypergraph with vertex set V and edge set E. $$S\subseteq V$$ S ⊆ V is a feedback vertex set (FVS) of H if $$H\setminus S$$ H \ S has no cycle and $$\tau _c(H)$$ τ c ( H ) denote the minimum cardinality of a FVS of H. Chen et al. [IWOCA,2016] has proven if H is a linear 3-uniform hypergraph with m edges, then $$\tau _c(H)\le m/3$$ τ c ( H ) ≤ m / 3 . In this paper, we furthermore characterize all the extremal hypergraphs with $$\tau _c(H)= m/3$$ τ c ( H ) = m / 3 holds. This result has a direct application to Tuza’s conjecture.

Keywords: Feedback Vertex Set (FVS); 3-Uniform Linear Hypergraphs; Extremal Hypergraphs (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-022-00893-8

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