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math.CO2026
An Erdős--Ko--Rado theorem for cross-intersecting families in the Euclidean inner product
Jiang-Chao Wan, Yi Wang
Let be the set of all -element subsets of the set and let be two cross-intersecting families,…
math.CO2026
A solution to Csikvári's conjecture and the largest matching root of -graphs
Jiang-Chao Wan, Yi Wang
In 2011, Csikvári [Electron. J. Combin. {\bf 18} (2011), P182] proved that among all graphs with a prescribed number of edges, the largest matching root is attained by a thresh…
math.CO2026
Perturbation of the largest matching root of hypergraphs
Jiang-Chao Wan, Yi Wang
The largest matching root of a -graph is the largest real root of its matching polynomial, which is equal to the maximum modulus of all the zeros of the matching polynomial. In…