Mathematics Colloquia and Seminars

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Helly’s theorem is perhaps one of the most widely used theorems in discrete geometry, and states that if every d+1 tuple of a finite family of convex sets in the euclidean space intersect, then all the sets of the family intersect. If not necessarily all, but a fraction of the (d+1)-tuples of the sets intersect, then the Fractional Helly Theorem states that a fraction of the sets must have a point in common. In this talk we will discuss an interesting behavior of fractional Helly’s theorem for the family of n-dimensional Boxes, (with edges parallel to the coordinate axes) an its relation with extremal graph theory.