Erdős-Gyárfás Conjecture for $P_{10}$-free Graphs

Zhiquan Hu, Changlong Shen

Let $P_{10}$ be a path on $10$ vertices. A graph is said to be $P_{10}$-free if it does not contain $P_{10}$ as an induced subgraph. The well-known Erdős-Gyárfás Conjecture states…