# A generalization of Vizing's Theorem?

**Conjecture**Let be a simple -uniform hypergraph, and assume that every set of points is contained in at most edges. Then there exists an -edge-coloring so that any two edges which share vertices have distinct colors.

Vizing's Theorem is equivalent to the above statement for . For higher dimensions, this problem looks difficult since the main tool used in the proof of Vizing's theorem (Kempe chains) do not appear to work.

## Reference

Could someone please add a reference? There should be some paper (or a conference talk?) where Rosenfeld proposed the conjecture.

-DOT