论文标题
$ k $均匀超图中的循环分解
Cycle decompositions in $k$-uniform hypergraphs
论文作者
论文摘要
我们表明，$ k $ - 均匀的超图表上的$ n $顶点的代码为$（2/3 + o（1））n $可以分解为紧密的周期，但要遵守琐碎的划分条件。作为推论，我们还显示这些图还包含了紧张的Euler之旅。顺便说一句，我们还研究了分解成紧密的路径。 此外，我们还证明了为任意$ k $ - 均匀的超图的边缘分解的吸收剂的替代条件，这应该具有独立的兴趣。
We show that $k$-uniform hypergraphs on $n$ vertices whose codegree is at least $(2/3 + o(1))n$ can be decomposed into tight cycles, subject to the trivial divisibility conditions. As a corollary, we show those graphs contain tight Euler tours as well. In passing, we also investigate decompositions into tight paths. In addition, we also prove an alternative condition for building absorbers for edge-decompositions of arbitrary $k$-uniform hypergraphs, which should be of independent interest.
