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BIRTHDAY
2009
Springer

On Path Partitions and Colourings in Digraphs

12 years 6 months ago
On Path Partitions and Colourings in Digraphs
We provide a new proof of a theorem of Saks which is an extension of Greene’s Theorem to acyclic digraphs, by reducing it to a similar, known extension of Greene and Kleitman’s Theorem. This suggests that the Greene-Kleitman Theorem is stronger than Greene’s Theorem on posets. We leave it as an open question whether the same holds for all digraphs, that is, does Berge’s conjecture concerning path partitions in digraphs imply the extension of Greene’s theorem to all digraphs (conjectured by Aharoni, Hartman and Hoffman)?
Irith Ben-Arroyo Hartman
Added 19 May 2010
Updated 19 May 2010
Type Conference
Year 2009
Where BIRTHDAY
Authors Irith Ben-Arroyo Hartman
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