Note: Bounding the feedback vertex number of digraphs in terms of vertex degrees

Authors:
Hermann Gruber
Affiliations:
-
Venue:
Discrete Applied Mathematics
Year:
2011

Citing 3
Cited 0

Hypergraph coverings and local colorings

Journal of Combinatorial Theory Series B
A note on greedy algorithms for the maximum weighted independent set problem

Discrete Applied Mathematics
A fixed-parameter algorithm for the directed feedback vertex set problem

Journal of the ACM (JACM)

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Abstract

The Turan bound (Turan (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.