8.14

题目：Prove that the following problem is NP-complete:

given an undirected graph G=[V,E]and an integer k,return a clique of size k as well as an independent set of size k,provided both exist.

解：

将最大团问题规约到该问题，假设要求任意图G(V,E)中大小为k的团，可以在图G中添加k个相互独立的顶点，得到新图G1。新加入的k个顶点确保图G1中存在大小为k的独立集同时又不影响到原图的团。因此该问题为NP完全问题。