Bounding the feedback vertex number of digraphs in terms of vertex degrees |
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Authors: | Hermann Gruber |
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Institution: | Knowledgepark AG, Leonrodstr. 68, 80636 München, Germany |
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Abstract: | The Turán bound (Turán (1941) 17]) is a famous result in graph theory, which relates the independence number of an undirected graph to its edge density. Also the Caro-Wei inequality (Caro (1979) 4] and Wei (1981) 18]), which gives a more refined bound in terms of the vertex degree sequence of a graph, might be regarded today as a classical result. We show how these statements can be generalized to directed graphs, thus yielding a bound on directed feedback vertex number in terms of vertex out-degrees and in terms of average out-degree, respectively. |
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Keywords: | Directed feedback vertex number Caro-Wei inequality Feedback set Acyclic set Induced DAG |
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