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<p>An <i>r</i>-graph <i>G</i> is called linear if every pair of vertices in <i>G</i> is contained in at most one edge. Let <i>F</i> and <i>H</i> be two linear <i>r</i>-graphs on <i>n</i> vertices. Then <i>H</i> is called <i>F</i>-free if it does not contain any copy of <i>F</i> as a subhypergraph. The linear Turán number ex<Stack> <sub><i>r</i></sub> <sup>lin</sup> </Stack>(<i>n, F</i>) of <i>F</i> is the maximum number of edges in any <i>F</i>-free linear <i>r</i>-graph on <i>n</i> vertices. A linear <i>r</i>-graph is acyclic if it can be constructed starting from one single edge then at each step adding a new edge that intersect the union of the vertices of the previous edges in at most one vertex. Recently, Gyárfás et al. initiated the study of the linear Turán numbers of acyclic linear 3-graphs. In this paper, we extend their results to acyclic linear 4-graphs.</p>

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The Linear Turán Numbers of Acyclic Linear 4-graphs

  • 期刊论文

  • 发表日期：

    2025年5月29日

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  • Lin-peng Zhang,
  • Li-gong Wang

摘要

An r-graph G is called linear if every pair of vertices in G is contained in at most one edge. Let F and H be two linear r-graphs on n vertices. Then H is called F-free if it does not contain any copy of F as a subhypergraph. The linear Turán number ex r lin (n, F) of F is the maximum number of edges in any F-free linear r-graph on n vertices. A linear r-graph is acyclic if it can be constructed starting from one single edge then at each step adding a new edge that intersect the union of the vertices of the previous edges in at most one vertex. Recently, Gyárfás et al. initiated the study of the linear Turán numbers of acyclic linear 3-graphs. In this paper, we extend their results to acyclic linear 4-graphs.