Seymour's Second Neighborhood Conjecture
Prior state unknown→proved
minimum out-degree 7; the conjecture is open in general
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combinatorics / Graph theory
Seymour's Second Neighborhood Conjecture
Seymour conjectured that every oriented graph has a vertex $x$ with $|N^{++}(x)| \ge |N^{+}(x)|$. It holds for oriented graphs of minimum out-degree exactly $7$, the first improvement to the out-degree threshold since Kaneko and Locke settled degree $6$ in 2001.
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Seymour conjectured that every oriented graph has a vertex $x$ with $|N^{++}(x)| \ge |N^{+}(x)|$. It holds for oriented graphs of minimum out-degree exactly $7$, the first improvement to the out-degree threshold since Kaneko and Locke settled degree $6$ in 2001.
minimum out-degree 7; the conjecture is open in general
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