Given a list of n natural numbers d1,d2,... ,dn, show how to decide in polynomial time whether there exists an undirected graph G = (V, E) whose node degrees are precisely the numbers d1, d2,...,dn. (That is, if V = {v1, v2,…, vn}, then the degree of vi should be exactly di.) G should not contain multiple edges between the same pair of nodes, or "loop" edges with both endpoints equal to the same node.
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