For $rgeq 2$, $lpha geq r-1$ and $kgeq 1$, let $c(r,lpha ,k)$ be the smallest integer $c$ such that the vertex set of any non-trivial $r$-uniform $k$-edge-colored hypergraph ${cal H}$ with $lpha ({cal H})=lpha$ can be covered by $c$ monochromatic connected components. Here $lpha({cal{H}})$ is the maximum cardinality of a subset $A$ of vertices in $cal{H}$ such that $A$ does not contain any edges. An old conjecture of Ryser is equivalent to $c(2,lpha,k)=lpha (r-1)$ and a recent result of Z. Király states that $c(r,r-1,k)=lceil rac{k}{r}ceil$ for any $rge 3$.
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机译：对于$ r geq 2 $，$ alpha geq r-1 $和$ k geq 1 $，令$ c（r， alpha，k）$为最小整数$ c $，使得顶点集为带有$ alpha（{ cal H}）= alpha $的任何非平凡的$ r $均匀$ k $边彩色超图$ { cal H} $都可以被$ c $单色连接的分量覆盖。这里$ alpha（{ cal {H}}）$是$ cal {H} $中顶点的子集$ A $的最大基数，因此$ A $不包含任何边。 Ryser的一个旧猜想等于$ c（2， alpha，k）= alpha（r-1）$，而Z.Király的最新结果指出$ c（r，r-1，k）= lceil frac {k} {r} rceil $对于任何$ r ge 3 $。
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