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In a directed graph, a '''dijoin''' is a set of arcs covering every directed cut. For a positive integer ''k'', a '''k-dijoin''' is a set of arcs containing ''k'' edges from every directed cut. A fundamental theorem about dijoins is the [[Lucchesi-Younger theorem]] on the minimum size of a dijoin.
The following observation (see e.g. Frank, Sebő and Tardos <ref>A. Frank, A. Sebő, É. Tardos, ''Covering directed and odd cuts'', Mathematical Programming Studies 22 (1984) 99-112. [http://dxwww.doispringerlink.orgcom/10.1007content/n8u48g68x8k4706p/BFb0121011 DOI Journal link], [http://www.cs.elte.hu/~frank/cikkek/FrankJ12.PDF Author link].</ref>) gives a useful property of inclusionwise minimal dijoins.
'''Lemma.''' Let ''D'' be a weakly connected digraph without cut arcs. If ''F'' is an inclusionwise minimal dijoin, then by reorienting the arcs of ''F'' we obtain a strongly connected digraph.
