Claims

../

1989_05_01_erdos_hajnal: Theorem 2 of Erdős and Hajnal (Discrete Math. 75 (1989)): a graph on n vertices with no K_{c log n, c log n} in it or its complement has at least 2^{n/4k} non-isomorphic induced subgraphs for k > 2c log 2 and n large.

1997_07_15_shelah: Theorem 1.3 of Shelah (J. Combin. Theory Ser. A 82 (1998)) proves that a graph on n vertices, n large, with no clique or independent set on c_1 log n vertices has at least 2^{c_2 n} non-isomorphic induced subgraphs.

---