Elsevier

Discrete Mathematics

Volume 243, Issues 1–3, 28 January 2002, Pages 213-216
Discrete Mathematics

Note
On dijoins☆

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Abstract

For every nonnegative integer arc weight function w, the minimum weight of a dicut is at least as large as the maximum number of dijoins such that no arc a is contained in more than w(a) of these dijoins. We give two examples of digraphs with strict inequality for some weight w and discuss the possibility that, together with an example due to Schrijver, these are the only “minimal” such examples.

Keywords

Dicut
Dijoin
Min–max theorem
Woodall's conjecture

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This work was supported in part by the Swiss National Research Fund (FNRS) and by NSF Grant DMI-9802773 and ONR Grant N00014-97-1-0196

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