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Seymour's Second Neighborhood Conjecture asserts that every oriented graphhas a vertex whose first out-neighborhood is at most as large as its secondout-neighborhood. Combs are the graphs having no induced $C_4$,$\overline{C_4}$, $C_5$, chair or $\overline{chair}$. We characterize combsusing dependency digraphs. We characterize the graphs having no induced $C_4$,$\overline{C_4}$, chair or $\overline{chair}$ using dependency digraphs. Thenwe prove that every oriented graph missing a comb satisfies this conjecture. Wethen deduce that every oriented comb and every oriented threshold graphsatisfies Seymour's conjecture.

The Second Neighborhood Conjecture for Oriented Graphs Missing Combs