Bruce Reed

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20242026

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math.CO2026

The Erd\H os-Sós conjecture in dense graphs

Bruce Reed, Maya Stein

The Erd\H os--Sós conjecture states that every $n$ -vertex graph with more than $(k - 2) n /2$ edges contains every $k$ -vertex tree. We prove that for every $γ$ there is an $n_{0}$ such t…

math.CO2026

The extremal cases of the Erd\H os--Sós conjecture

Bruce Reed, Maya Stein

The Erd\H os--Sós conjecture states that every $n$ -vertex graph $G$ with more than $(k - 2) n /2$ edges contains every $k$ -vertex tree. We solve the extremal cases of this conjecture,…