For k-subset families that cross-intersect but each lacks a common element, their size product is bounded by the square of the Hilton-Milner number when k is at least 8.
Hilton, The Erd˝ os-Ko-Rado Theorem with valency conditions, unpublished manuscript
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
math.CO 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Any intersecting k-graph with covering number at least three satisfies the stated binomial-coefficient upper bound for all n greater than or equal to 2k.
citing papers explorer
-
A product version of the Hilton-Milner Theorem II
For k-subset families that cross-intersect but each lacks a common element, their size product is bounded by the square of the Hilton-Milner number when k is at least 8.
-
Intersecting families with covering number three II
Any intersecting k-graph with covering number at least three satisfies the stated binomial-coefficient upper bound for all n greater than or equal to 2k.