3 papers
math.CO2026
Polynomial positivity cones for Coxeter roots and walks in trees
Dongxiu Cai, Zhenbo Chen, Jiasheng Zeng +1
For a finite simple graph and an integer , let denote the number of walks of length . We prove the conjecture of Täubig, Weihmann, Kosub, Hemmecke, and Mayr…
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
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=…