What is Hypergraph coloring?

Hypergraph colouring is defined as follows. Let $H=(V, E)$ be a hypergraph such that $\Vert V\Vert = n$ . Then $C=\{c_1, c_2, \ldots, c_n\}$ (??) is a proper colouring of $H$ if and only if, for all $e \in E, \vert e\vert > 1,$ there exists $v_i, v_j \in e$ such that $c_i \neq c_j$ .

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

posted on 2012-08-22 15:44 york_hust 阅读(181) 评论(0) 编辑收藏举报