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Motivated by Hadwiger's conjecture, we prove that every $n$-vertex graph $G$with no independent set of size three contains an $\lceil n/2\rceil$-vertexsimple minor $H$ with $$0.98688 \cdot \binom{|V(H)|}{2} - o(n^2)$$ edges.

Dense minors of graphs with independence number two