The Ramsey Number for 4-Uniform Tight Cycles
The Ramsey Number for 4-Uniform Tight Cycles
复制标题
4-均匀紧循环的拉姆齐数
DOI：
10.1007/978-3-030-83823-2_69
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Vincent Pfenninger
中科院分区：
文献类型：
--
作者：
A. Lo;Vincent Pfenninger
一个$k$一致紧环是一个$k$图，它的顶点具有循环顺序，使得它的边恰好是该顺序下$k$连续顶点的集合。$k$-均匀紧路径是通过从$k$-均匀紧循环中删除一个顶点而得到的$k$-图。我们证明了$4n$顶点上$4$-均匀紧循环的Ramsey数为$(5 +o(1))n$。这是渐近紧的。这个结果也意味着$n$顶点上$4$-均匀紧路径的Ramsey数为$(5/4 + o(1))n$。
A $k$-uniform tight cycle is a $k$-graph with a cyclic ordering of its vertices such that its edges are precisely the sets of $k$ consecutive vertices in that ordering. A $k$-uniform tight path is a $k$-graph obtained by deleting a vertex from a $k$-uniform tight cycle. We prove that the Ramsey number for the $4$-uniform tight cycle on $4n$ vertices is $(5 +o(1))n$. This is asymptotically tight. This result also implies that the Ramsey number for the $4$-uniform tight path on $n$ vertices is $(5/4 + o(1))n$.
DOI：
10.4153/s0008414x20000632
发表时间：
2021
期刊：
Canadian Journal of Mathematics
影响因子：
--
作者：
Füredi, Zoltán;Jiang, Tao;Kostochka, Alexandr;Mubayi, Dhruv;Verstraëte, Jacques
通讯作者：
Verstraëte, Jacques
凸几何超图中的紧路径
影响因子：
--
作者：
Mubayi, Dhruv;Füredi, Zoltán;Verstraëte, Jacques;Kostochka, Alexandr;Jiang, Tao
通讯作者：
Jiang, Tao