13 papers
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…
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…
On degree bounds of -uniform hypergraphs with bounded matching number
Haixiang Zhang, Mengyu Cao, Mei Lu
The paper establishes degree sequence and Ore-degree conditions that guarantee a k‑uniform hypergraph contains a matching of a given size, improving previous bounds and showing the…
Generalizations of the ErdÅs Matching Conjecture for the -Matching Number
Mengyu Cao, Mei Lu, Haixiang Zhang
The paper determines the maximum number of edges in a k‑uniform hypergraph with a prescribed t‑matching number, extending the Erdős Matching Conjecture, and also identifies the sec…