Mengyue Cao

works on

extremal combinatorics 2 hypergraph matching 2 intersecting families 2 codegree 1 degree conditions 1 degree powers 1 erdos-ko-rado theorem 1 Erdős-Ko-Rado theorem 1 erdos matching conjecture 1 extremal set theory 1 finite fields 1 hilton-milner theorem 1

From the 4 of 12 linked papers with an AI index.

collaborators

12 papers

math.CO2026

Erdős--Ko--Rado and Hilton--Milner Theorems in the Partition Lattice

Mengyu Cao, Jiaqi Liao, Haixiang Zhang

Let $M_{n} = M (K_{n + 1})$ be the graphic matroid of the complete graph, and let $F_{k} (M_{n})$ be its rank- $k$ flats. We study families $A \subseteq F_{k} (M_{n})$ sa…

math.CO2026

Entropy Transference for Rainbow- $H$ -Free Colourings of Random Graphs

Mengyu Cao, Mei Lu, Haixiang Zhang

Let $H$ be a fixed graph with $e (H) \geq 3$ that contains two adjacent edges, and let $ℓ \geq e (H)$ be fixed. We establish an entropy-transference principle for rainbow- $H$ -free edge…

math.CO2026

On ErdÅs--Ko--Rado and Hilton--Milner Theorems for Direct Products

Tian Yao, Mengyu Cao, Kaishun Wang

Let $X = X_{1} \cup ˙ \dots \cup ˙ X_{p}$ and $H (k) = {F \subseteq X : ∣ F \cap X_{i} ∣ = k_{i} for every i}$ . We study $t$ -intersecting families in…

math.CO2026

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…

math.CO2026

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…

math.CO2026

Matchings and Near-Optimal 2-Factor Packings in Percolated Vertex-Transitive Graphs

Mengyu Cao, Mei Lu, Xiamiao Zhao

Let $G$ be a connected simple vertex-transitive graph on $n$ vertices with degree $d$ , and let $G_{p}$ be the random spanning subgraph obtained by retaining each edge of $G$ independ…

Erdős--Ko--Rado and Hilton--Milner Theorems in the Partition Lattice

Entropy Transference for Rainbow-H-Free Colourings of Random Graphs

On ErdÅs--Ko--Rado and Hilton--Milner Theorems for Direct Products

Convex Transference for Degree Powers in Extremal Set Systems

Projective Ore-Degree Conditions for Intersection Theorems in Vector Spaces

Matchings and Near-Optimal 2-Factor Packings in Percolated Vertex-Transitive Graphs

Entropy Transference for Rainbow- $H$ -Free Colourings of Random Graphs

On ErdÅs--Ko--Rado and Hilton--Milner Theorems for Direct Products