What is Hypergraph coloring?

Hypergraph colouring is defined as follows. Let  be a hypergraph such that . Then (??) is a proper colouring of  if and only if, for all  there exists  such that .

In other words: For every edge in the graph having at least two nodes as endpoints, the nodes this edge connects are not all of the same color.

A coloring of a hypergraph is a mapping of vertices to colors such that no hyperedge is monochromatic(单色的)

超边着色问题: H=(V,E),有n个点,有k种颜色,给每个点涂上一种颜色,使得任何一条边的所有点都不是相同的颜色