combinatorial bounds 1cover graphs 1critical hypergraphs 1cross-intersecting families 1extremal hypergraph theory 1extremal set theory 1hilton-milner theorem 1intersecting families 1product extremal problems 1t-intersecting 1
From the 2 of 3 linked papers with an AI index.
3 papers
math.CO2026
An improved range for the maximum critically -intersecting hypergraphs
Lu Lu, Rongrong Lu, Qifan Wang +1
The paper proves that for k-uniform hypergraphs that are t‑intersecting and t‑critical, the maximum number of edges is bounded by \(\binom{k+d}{d}\) when k > 30·d², confirming Fran…
math.CO2026
On a conjecture regarding the product version of the Hilton-Milner theorem
Xucheng Bu, Lihua Feng, Zejun Huang +2
The paper studies a conjecture on the product version of the Hilton‑Milner theorem for non‑trivial cross‑intersecting families, disproving it in a linear range of parameters and co…
math.CO2026
Improved bound on symmetric differences of intersecting families
Lihua Feng, Zejun Huang, Qifan Wang +1
For a family , it is called intersecting if for all . We use $\mathcal{SD}(\mathcal{F}) = \{F \triangle G : F, G \in \math…