From the 4 of 10 linked papers with an AI index.
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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…
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…
Matchings and Near-Optimal 2-Factor Packings in Percolated Vertex-Transitive Graphs
Mengyu Cao, Mei Lu, Xiamiao Zhao
Let be a connected simple vertex-transitive graph on vertices with degree , and let be the random spanning subgraph obtained by retaining each edge of independ…
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…