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arXiv · 0905.2644

Paths and stability number in digraphs

Jacob Fox·Benny Sudakov
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Abstract

The Gallai-Milgram theorem says that the vertex set of any digraph with stability number k can be partitioned into k directed paths. In 1990, Hahn and Jackson conjectured that this theorem is best possible in the following strong sense. For each positive integer k, there is a digraph D with stability number k such that deleting the vertices of any k-1 directed paths in D leaves a digraph with stability number k. In this note, we prove this conjecture.

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Jacob Fox, Benny Sudakov. 2009-06-14. Paths and stability number in digraphs. https://arxiv.org/abs/0905.2644

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