Abstract
Let Sk(n) be the maximum number of orientations of an n-vertex graph G in which no copy of Kk is strongly connected. For all integers n, k≥4 where n≥5 or k≥5, we prove that Sk(n)=2tk−1(n), where tk−1(n) is the number of edges of the n-vertex (k−1)-partite Turán graph Tk−1(n), and that Tk−1(n) is the only n-vertex graph with this number of orientations. Furthermore, S4(4)=40 and this maximality is achieved only by K4.
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