论文标题
朝着Lehel的猜想，以实现4均匀的紧身周期
Towards Lehel's conjecture for 4-uniform tight cycles
论文作者
论文摘要
$ k $均匀的紧身周期是$ k $均匀的超图，其顶点循环订购，因此其边缘是订购中$ k $连续的顶点形成的所有尺寸$ k $的集合。我们证明，每个红色蓝色边缘色$ k_n^{（4）} $都包含一个红色和蓝色的紧身周期，它们是顶点 - 偶数，一起覆盖$ n-o（n）$ vertices。此外，我们证明了每个红蓝色边缘色$ k_n^{（5）} $包含四个单色紧身循环，它们是顶点 - 偶数，一起覆盖$ n-o（n）$ pertices。
A $k$-uniform tight cycle is a $k$-uniform hypergraph with a cyclic ordering of its vertices such that its edges are all the sets of size $k$ formed by $k$ consecutive vertices in the ordering. We prove that every red-blue edge-coloured $K_n^{(4)}$ contains a red and a blue tight cycle that are vertex-disjoint and together cover $n-o(n)$ vertices. Moreover, we prove that every red-blue edge-coloured $K_n^{(5)}$ contains four monochromatic tight cycles that are vertex-disjoint and together cover $n-o(n)$ vertices.
