2026/07/30 by Lu Lu, Rongrong Lu, Qifan Wang +1 · 1 voice
Mathematics · #math.CO
arxiv created 2026/07/30 · arxiv updated 2026/07/31
Let k>t≥ 1 be integers and set d=k-t. A k-uniform hypergraph \mathcal F is called t-intersecting if any two edges intersect in at least t vertices, and is called t-critical if its minimum t-transversal has size k. Frankl proved that, for k≥ d4,|\mathcal F|≤ \binomk+dd, with equality only for the complete k-graph on k+d vertices, and conjectured that the same conclusion should hold when k>c d2 for some constant c. In this paper we confirm this conjecture for c=30. The proof relies on Frankl's fixed-edge decomposition and Füredi's pseudo-sunflower method.