Tight bound on treedepth in terms of pathwidth and longest path
Meike Hatzel, Gwenaël Joret, Piotr Micek, Marcin Pilipczuk, Tors·2023-02-07·via math.CO updates on arXiv.org
We show that every graph with pathwidth strictly less than $a$ that contains no path on $2^b$ vertices as a subgraph has treedepth at most $10ab$. The bound is best possible up to a constant factor.
