Linearly $\chi$-Bounding $(P_6,C_4)$-Free Graphs

Serge Gaspers, Shenwei Huang

Given two graphs $H_1$ and $H_2$, a graph $G$ is $(H_1,H_2)$-free if it contains no subgraph isomorphic to $H_1$ or $H_2$. Let $P_t$ and $C_s$ be the path on $t$ vertices and the c…