Ramsey-type problems on induced covers and induced partitions toward the Gyárfás-Sumner conjecture

Shuya Chiba, Michitaka Furuya

Gyárfás and Sumner independently conjectured that for every tree $T$, there exists a function $f_T:\mathbb{N}\to \mathbb{N}$ such that every $T$-free graph $G$ satisfie…