European Journal of Combinatorics ( IF 1.0 ) Pub Date : 2020-05-30 , DOI: 10.1016/j.ejc.2020.103161 Zixiang Xu , Tao Zhang , Gennian Ge
Recently, several hypergraph Turán problems were solved by the powerful random algebraic method. However, the random algebraic method usually requires some parameters to be very large, hence we are concerned about how these Turán numbers depend on such large parameters of the forbidden hypergraphs. In this paper, we determine the dependence on such specified large constant for several hypergraph Turán problems. More specifically, for complete -partite -uniform hypergraphs, we show that if is sufficiently larger than then For complete bipartite -uniform hypergraphs, we prove that if is sufficiently larger than we have In particular, our results imply that the famous Kővári–Sós–Turán’s upper bound has the correct dependence on large . The main approach is to construct random multi-hypergraph via a variant of random algebraic method.
中文翻译:
通过多重超图的构造来解决Turán问题的一些紧下界
最近,通过强大的随机代数方法解决了一些超图Turán问题。但是,随机代数方法通常要求某些参数非常大,因此我们担心这些Turán数如何取决于禁止超图的如此大参数。在本文中,我们确定了几个超图Turán问题对这样指定的大常数的依赖性。更具体地说,完整-部分 -一致的超图,我们证明 足够大于 然后 对于完全二分 -一致超图,我们证明 足够大于 我们有 特别是,我们的结果暗示着著名的克瓦里(Kővári–Sós–Turán)的上限 正确依赖大 。主要方法是通过随机代数方法的变体构造随机多超级图。