Treedepth and 2-treedepth in graphs with no long induced paths

Jędrzej Hodor, Freddie Illingworth, Tomasz Mazur

Huynh, Joret, Micek, Seweryn, and Wollan (Combinatorica, 2022) introduced a graph parameter, later referred to as 2-treedepth and denoted ${\mathrm{td}}_2(\cdot )$. The parameter is t…