Question: Prove that the following problem is NP-complete: Given a graph G, and an integer k, find whether or not graph G has a spanning degree

Prove that the following problem is NP-complete:

Given a graph G, and an integer k, find whether or not graph G has a spanning degree where the maximum degree of any node is k.

(Hint: Show a reduction from one of the following known NP-complete problems: Vertex Cover, Ham Path or SAT.)

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