Week17

Problem–8.19

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

answer:

我们可以将团问题规约到KITE问题。若要求图G(V,E)的最大团，可以在图G中添加|V|个新节点，并将每个新顶点都连向原图中不同的某个顶点，供形成|V|条新边，这样就得了一个新图G‘。容易看出，在G’中存在大小为2g的kite当且仅当G中存在大小为g的团。