This comes from a comment made by user bof in [this thread][1]. 

Let $X$ be a set, define ${\cal P}_2(X) = \big\{\{a, b\}: a\neq b\in X\big\}$.

Consider the statement

>> ${\sf (S)}$ If $X$ is an infinite set, then there is a bijection $\varphi: {\cal P}_2(X)\to X$.

Does ${\sf (S)}$ imply ${\sf (AC)}$?

  [1]: https://mathoverflow.net/questions/228159/edge-chromatic-number-of-hypergraphs