Cop number of $P_k$-free graphs without a claw or a fork

Uttam K. Gupta, Dinabandhu Pradhan, Rashmi Rekha Swain

In 2019, Liu proved that the cop number of any $(P_k,claw)$-free graph is at most $k-3$. In 2026, Clow and Meger improved and generalized the result of Liu by showing that every c…