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Let $r \geq 2$, $n$ and $k$ be integers satisfying $k \leq \frac{r-1}{r}n$.In the original arXiv version of this note we suggested a conjecture that thefamily of all $k$-subsets of an $n$-set cannot be partitioned into fewer than$\lceil n-\frac{r}{r-1}(k-1) \rceil$ $r$-wise intersecting families. We notedthat if true this is tight for all values of the parameters, that the case$r=2$ is Kneser's conjecture, proved by Lov\'asz, and observed that theassertion also holds provided $r$ is either a prime number or a power of $2$.We have recently learned, however, that the assertion of the conjecture for allvalues of the parameters follows from a recent result of Azarpendar and Jafari\cite{AJ}.

Partitioning all $k$-subsets into $r$-wise intersecting families