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A "cosmic kite" of size k consists of a clique of k nodes with a path of k nodes that unfolds from one of the nodes in the clique.

Cosmic Kite as decision problem Input: a graph G = (V, E) and a parameter k ∈ N. Question: Does G contain a cosmic kite of cardinality at least k?

Show that Cosmic Kite is NP-complete

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Hint: Reduce from Clique. To every node, connect a path of $k$ vertices.

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