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The Turan bound is a famous result in graph theory, which relates theindependence number of an undirected graph to its edge density. Also theCaro-Wei inequality, which gives a more refined bound in terms of the vertexdegree sequence of a graph, might be regarded today as a classical result. Weshow how these statements can be generalized to directed graphs, thus yieldinga bound on directed feedback vertex number in terms of vertex outdegrees and interms of average outdegree, respectively.

Bounding the Feedback Vertex Number of Digraphs in Terms of Vertex Degrees