Counting Points of Slope Varieties over Finite Fields

Thomas Enkosky


The slope variety of a graph is an algebraic set whose points correspond to drawings of that graph. A complement-reducible graph (or cograph) is a graph without an induced four-vertex path. We construct a bijection between the zeroes of the slope variety of the complete graph on $n$ vertices over $\mathbb{F}_2$, and the complement-reducible graphs on $n$ vertices.

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