Counting points of slope varieties over finite fields

Mathematics – Combinatorics

Scientific paper

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9 pages, 5 figures

Scientific paper

The slope variety of a graph is an algebraic set whose points correspond to
drawings of a 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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