On 3-graphs with no four vertices spanning exactly two edges

Let (Formula presented.) denote the 3-uniform hypergraph with 4 vertices and 2 edges. Answering a question of Alon and Shapira, we prove an induced removal lemma for (Formula presented.) having polynomial bounds. We also prove an Erdős–Hajnal-type result: Every induced (Formula presented.) -free hypergraph on (Formula presented.) vertices contains a clique or an independent set of size (Formula presented.) for some absolute constant (Formula presented.). In the case of both problems, (Formula presented.) is the only nontrivial (Formula presented.) -uniform hypergraph with (Formula presented.) which admits a polynomial bound.