Cop number of $2K_2$-free graphs

Vaidy Sivaraman, Stephen Testa

Published 2019-03-27Version 1

We prove that the cop number of a $2K_2$-free graph is at most $2$ if it has diameter $3$ or does not have an induced cycle of length $k$, where $k \ \in \{3,4,5\}$. We conjecture that the cop number of every $2K_2$-free graph is at most $2$.