How redundant is Mantelâ s Theorem

Shagnik Das
One of the all-time combinatorial classics, Mantel's Theorem asserts that if one forbids an $n$-vertex graph $G$ from containing any triangle, then $G$ can have at most $\frac{n^2}{4}$ edges. In this talk, we explore an extension of this theorem suggested by Gil Kalai. Suppose, for some $0 \le m \le \binom{n}{3}$, we can only forbid $m$ of the triangles from appearing in $G$. What choice of the forbidden triangles then minimises the maximum number of...
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