Lagrangian densities of linear forests and Turan numbers of their extensions
Lagrangian densities of linear forests and Turan numbers of their extensions
复制标题
线性森林的拉格朗日密度及其扩展的图兰数
DOI：
10.1002/jcd.21687
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发表时间：
2020
影响因子：
0.7
通讯作者：
Wu Biao
中科院分区：
文献类型：
--
作者：
Hu Sinan;Peng Yuejian;Wu Biao
超图的拉格朗日函数在超图极值问题中一直是一个有用的工具。近年来，超图的拉格朗日密度及其扩张的图兰数一直是研究的热点。然而，确定一个超图的拉格朗日密度并不是一件容易的事情，即使对于一个“简单的”超图也是如此。例如，确定的拉格朗日密度等价于确定的图兰密度(图兰的一个长期猜想)。Hefetz和Keevash研究了尺寸为2的3一致匹配的拉格朗日密度。Pikhurko确定了长度为2的4一致紧路的拉格朗日密度，从而证实了Frankl和Füredi关于这种情况下一致广义三角形的图兰数的猜想。考虑其他“基本”超图的拉格朗日密度是很自然和有趣的。本文确定了一类3-一致线性森林的拉格朗日密度。对于正整数和，设3-一致的两条不相交的边的线性路径的不相交并。本文确定了任意子3的拉格朗日密度。应用Brandt，Irwin和酱所用的Pikhurko转移引理的一个修正形式，我们得到了它们的扩张的图兰数。
The Lagrangian of a hypergraph has been a useful tool in hypergraph extremal problems. Recently, Lagrangian densities of hypergraphs and Turán numbers of their extensions have been studied actively. However, determining the Lagrangian density of a hypergraph is not an easy task even for a “simple” hypergraph. For example, to determine the Lagrangian density ofis equivalent to determine the Turán density of(a long standing conjecture of Turán). Hefetz and Keevash studied the Lagrangian density of the 3‐uniform matching of size 2. Pikhurko determined the Lagrangian density of a 4‐uniform tight path of length 2 and this led to confirm the conjecture of Frankl and Füredi on the Turán number of the‐uniform generalized triangle for the case. It is natural and interesting to consider Lagrangian densities of other “basic” hypergraphs. In this paper, we determine the Lagrangian densities for a class of 3‐uniform linear forests. For positive integersand, letbe the disjoint union of a 3‐uniform linear path of lengthandpairwise disjoint edges. In this paper, we determine the Lagrangian densities offor anyandor 3. Applying a modified version of Pikhurko's transference argument used by Brandt, Irwin, and Jiang, we obtain the Turán numbers of their extensions.