Four-vertex obstruction to polychromatic three-colouring
= Four-vertex obstruction to polychromatic three-colouring
Take every three-element subset of a four-element vertex set as a <hypergraph edge>. Any three-colouring repeats a colour on two vertices. A triple containing that pair cannot contain all three colours. Thus this <uniform hypergraph> has no polychromatic three-colouring, although each edge meets only three other edges.