2 problems

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Simonovits–Sós conjecture for 3-AP- and triangle-intersecting families
Let $[n]=\{1,\ldots,n\}$ , and let $\mathcal{A}$ be a family of subsets of $[n]$ or a family of labelled graphs on $n$ vertices. In the first setting, require that every pair of set…
Conjecturerefutedarithmetic-progressions extremal-combinatorics intersection-problemsarXiv posted 2 days ago
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The modified-design conjecture for the Erdős–Sós problem
Let $k$ be the uniformity and let $\ell$ be the forbidden intersection size in the Erdős–Sós problem, with … An extremal family is a family of $k$ -sets with no two members intersec…
Conjectureopendesign-theory extremal-set-theory intersection-problemsarXiv posted 2 days ago

Simonovits–Sós conjecture for 3-AP- and triangle-intersecting families