20 citations · 69 across the 36 of their papers we have counts for
5 papers · 1 filter
On the structure of subsets of the discrete cube with small edge boundary
David Ellis, Nathan Keller, Noam Lifshitz
The edge isoperimetric inequality in the discrete cube specifies, for each pair of integers and , the minimum size of the edge boundary of an -element subset of…
On the union of intersecting families
David Ellis, Noam Lifshitz
A family of sets is said to be \emph{intersecting} if any two sets in the family have nonempty intersection. In 1973, Erdős raised the problem of determining the maximum possible s…
A Note on Large H-Intersecting Families
Nathan Keller, Noam Lifshitz
A family of graphs on a fixed set of vertices is called triangle-intersecting if for any , the intersection contains a triangle. More generall…
Stability for the Complete Intersection Theorem, and the Forbidden Intersection Problem of Erdős and Sós
David Ellis, Nathan Keller, Noam Lifshitz
A family of sets is said to be -intersecting if for any . The seminal Complete Intersection Theorem of Ahlswede and Khachatrian (1997) gives t…
Stability versions of Erdős-Ko-Rado type theorems, via isoperimetry
David Ellis, Nathan Keller, Noam Lifshitz
Erdős-Ko-Rado (EKR) type theorems yield upper bounds on the sizes of families of sets, subject to various intersection requirements on the sets in the family. Stability versions of…