Abstract
AbstractIn 1963, Tibor Gallai [9] asked whether every strongly connected directed graph D is spanned by α directed circuits, where α is the stability of D. We give a proof of this conjecture using a new structure for digraphs called cyclic orders. Three min-max theorems for cyclic orders are derived.KeywordsChromatic NumberCyclic OrderForward PathMaximal AntichainAcyclic DigraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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