Graphs with no long claws: An improved bound for the analog of the
Gy\'{a}rf\'{a}s' path argument
Graphs with no long claws: An improved bound for the analog of the
Gy\'{a}rf\'{a}s' path argument
For a fixed integer $t \geq 1$, a ($t$-)long claw, denoted $S_{t,t,t}$, is the unique tree with three leaves, each at distance exactly $t$ from the vertex of degree three. Majewski et al. [ICALP 2022, ACM ToCT 2024] proved an analog of the Gy\'{a}rf\'{a}s' path argument for $S_{t,t,t}$-free graphs: given …