From the 4 of 14 linked papers with an AI index.
14 papers
A Sharp Spectral Erdős--Ko--Rado Theorem for Uniform Hypergraphs
Mengyu Cao, Mei Lu, Haixiang Zhang
The spectral Erdős--Ko--Rado problem asks for the largest adjacency-tensor spectral radius of a -intersecting -uniform family. Keevash, Lenz and Mubayi proved that, for fixed…
Erdős--Ko--Rado and Hilton--Milner Theorems in the Partition Lattice
Mengyu Cao, Jiaqi Liao, Haixiang Zhang
Let be the graphic matroid of the complete graph, and let be its rank- flats. We study families sa…
Entropy Transference for Rainbow--Free Colourings of Random Graphs
Mengyu Cao, Mei Lu, Haixiang Zhang
Let be a fixed graph with that contains two adjacent edges, and let be fixed. We establish an entropy-transference principle for rainbow--free edge…
On Erdős--Ko--Rado and Hilton--Milner Theorems for Direct Products
Tian Yao, Mengyu Cao, Kaishun Wang
We investigate -intersecting families in direct-product set systems obtained by prescribing the number of selected elements in each part of a partitioned ground set. For a finit…
Convex Transference for Degree Powers in Extremal Set Systems
Mengyu Cao, Mei Lu, Haixiang Zhang
The paper introduces a discrete two‑moment interpolation technique to bound sums of degree powers in intersecting families and shows that full star families uniquely maximize these…
Projective Ore-Degree Conditions for Intersection Theorems in Vector Spaces
Mengyu Cao, Mei Lu, Xuyang Yan +1
The paper introduces a projective Ore-degree measure for families of k‑dimensional subspaces over a finite field and proves sharp analogues of the Erdős–Ko–Rado and Hilton–Milner i…