Proof Of A Conjecture Of Erdős On Triangles In Set-Systems
Proof Of A Conjecture Of Erdős On Triangles In Set-Systems
A triangle is a family of three sets A,B,C such that A∩B, B∩C, C∩A are each nonempty, and $$ A \cap B \cap C = \emptyset $$ . Let $$ {\user1{\mathcal{A}}} $$ be a family of r-element subsets of an n-element set, containing no triangle. Our main result implies that …