3 papers
math.CO2026
The Equality Cases for the Grone-Merris-Bai Theorem
Dongxiu Cai, Zhengbo Chen, Jia Yang +1
The Grone--Merris inequality, conjectured by Grone and Merris~(1994) and first proved by Bai~(2011), states that for every graph of order and every , $\sum_{i=…
math.CO2026
The Equality Cases For the Laplacian Conjecture of Brouwer
Dongxiu Cai, Zhengbo Chen, Jia Yang +1
The Laplacian conjecture of Brouwer asserts that for any graph \(G\) of order n with \(m\) edges, the sum of the \(k\) largest Laplacian eigenvalues satisfies \(s_k(G) \le m + \bin…
math.CO2026
Sharp Bounds for Guiduli-Type Hereditary Spectral Problems
Dongxiu Cai, Jiasheng Zeng, Xiao-Dong Zhang
Guiduli asked in 1996 the following problem concerning the maximum spectral radius of a graph under hereditary density constraints. If an -vertex graph satisfies $e(H)\le c|…