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Seymour's Second Neighborhood Conjecture (SNC) asserts that every orientedgraph has a vertex whose first out-neighborhood is at most as large as itssecond out-neighborhood. In this paper, we prove that if $G$ is a graphcontaining no induced $C_4$, $\overline{C_4}$, $S_3$, chair and$\overline{chair}$, then every oriented graph missing $G$ satisfies thisconjecture. As a consequence, we deduce that the conjecture holds for everyoriented graph missing a threshold graph, a generalized comb or a star.

The Second Neighborhood Conjecture for Oriented Graphs Missing $\{C_{4}, \overline{C_{4}}, S_{3},$ chair and co-chair$\}$-Free Graph