算法概率课后题 8.14

Ex.8.14 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.

答：可以将最大团问题归约到此问题。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G'。这新加的k个顶点保证了图G'存在大小为k的独立集，同时又不影响到原图的团。