On Greene-Kleitman's theorem for general digraphs
نویسندگان
چکیده
Aharoni, R. and I. Ben-Arroyo Hartman, On Greene-Kleitman’s theorem for general digraphs, Discrete Mathematics 120 (1993) 13-24. Linial conjectured that Greene-Kleitman’s theorem can be extended to general digraphs. We prove a stronger conjecture of Berge for digraphs having k-optimal path partitions consisting of ‘long’ paths. The same method yields known results for acyclic digraphs, and extensions of various theorems of Greene and Frank to acyclic digraphs.
منابع مشابه
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 pa...
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 120 شماره
صفحات -
تاریخ انتشار 1993