Question: Let k be a positive integer. Prove that a(n undirected) graph G has an orientation in which the outdegree and the indegree of each vertex

Let k be a positive integer. Prove that a(n undirected) graph G has an orientation in which the outdegree and the indegree of each vertex is at most k if and only if (G) 2k. (Hint: For the more difficult part of the proof, consider first 2k-regular graphs.)

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