2 research outputs found
Paths and stability number in digraphs
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.Comment: 3 page
Reviewed by Pooya Hatami References
Lexicographic products and a conjecture of Hahn and Jackson. (English summary