Erdős–Hajnal for graphs with no 5-hole - Chudnovsky, M; Scott, A; Seymour, P; Spirkl, S (London Mathematical Society, 2023)
The Erdős–Hajnal conjecture says that for every graph 𝐻 there exists 𝜏>0 such that every graph𝐺not con-taining𝐻as an induced subgraph has a clique or stable set of cardinality at least |𝐺|𝜏. We prove that this is true when 𝐻 is a cycle of length five. We also prove several further results: for instance, that if 𝐶 is a cycle and 𝐻 is the complement of a forest, there exists 𝜏>0 such that every graph 𝐺 containing neither of 𝐶,𝐻 as an induced subgraph has a clique or stable set of cardinality at least|𝐺|𝜏.