SIAM Journal on Discrete Mathematics, Volume 34, Issue 2, Page 1460-1471, January 2020.
Confirming a conjecture of Gyárfás, we prove that, for all natural numbers $k$ and $r$, the vertices of every $r$-edge-colored complete $k$-uniform hypergraph can be partitioned into a bounded number (independent of the size of the hypergraph) of monochromatic tight cycles. We further prove that, for all natural numbers $p$ and $r$, the vertices of every $r$-edge-colored complete graph can be partitioned into a bounded number of $p$th powers of cycles, settling a problem of Elekes, Soukup, Soukup, and Szentmiklóssy [Discrete Math., 340 (2017), pp. 2053--2069]. In fact we prove a common generalization of both theorems which further extends these results to all host hypergraphs of bounded independence number.

中文翻译：

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将边色超图划分为几个单色紧周期

SIAM离散数学杂志，第34卷，第2期，第1460-1471页，2020年1月。
证实了Gyárfás的猜想，我们证明，对于所有自然数$ k $和$ r $，每个$ r $-的顶点可以将边缘着色的完整$ k $统一超图划分为单色紧周期的有界数（与超图的大小无关）。我们进一步证明，对于所有自然数$ p $和$ r $，每个$ r $ -edge-coloured完整图的顶点都可以划分为无穷大的$ p $ th次幂，从而解决了Elekes，Soukup，Soukup和Szentmiklóssy[Discrete Math。，340（2017），第2053--2069页]。实际上，我们证明了这两个定理的共同概括，将这些结果进一步扩展到有界独立数的所有宿主超图。