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Packing directed circuits fractionally. (English) Zbl 0826.05031
A fractional circuit packing of value \(v\) of a directed graph \(G\) is a function that assigns a non-negative rational number \(q(C)\) to each circuit \(C\) such that (i) the sum of \(q(C)\) over all circuits containing any given vertex is at most one, and (ii) the sum of \(q(C)\) over all circuits is \(v\). The author shows that if every fractional circuit packing of \(G\) has value at most \(k\) where \(k\geq 1\), then there exists a set of at most \(4k\log(4k) \log\log_2(4k)\) vertices of \(G\) that meets every circuit.

MSC:
05C20 Directed graphs (digraphs), tournaments
05C38 Paths and cycles
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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