Dense minors of graphs with independence number two

Paul Seymour; Sergey Norin

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Dense minors of graphs with independence number two

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arxiv 2206.00186 v1 pith:DRYJ4WIS submitted 2022-06-01 math.CO

Sergey Norin , Paul Seymour This is my paper · ORCID

classification math.CO

keywords vertexbinomcdotconjecturecontainsdenseedgesevery

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abstract

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

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