Question: Let T = (V, E) be a tournament with v V of maximum out degree. If w V and w v, prove

Let T = (V, E) be a tournament with v ∈ V of maximum out degree. If w ∈ V and w ≠ v, prove that either (v, w) ∈ E or there is a vertex y in V where y ≠ v, w, and (v, y), (y, w) ∈ E. (Such a vertex v is called a king for the tournament.

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