2017算法课.作业(8.19)

题目:


A ktie is a graph on even number of vertices, say 2n, in which n of the vertices form a clique and the remaining n vectors are connected in a tail that consisits of a path joined to one of the vertices of the clique.Given a graph and a goal g, the Kite problem asks for subgraph which is a kite and which contains 2g nodes.Prove that kite is NP-complete.


解答:可以将团问题归结到kite问题上,若要求图G(V,E)的最大团,类似于8.14,可以在图G中添加|V|个顶点,并将每个新顶点都连向原图中不同的某个顶点,共形成了V条新边,这样就得到了一个新图G',容易看出,在G‘中存在大小为2g的kite,当且仅当存在大小为g的团。

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