Xiao-Dong Zhang

collaborators

5 papers

math.CO2026

A sharp bound for the least signless Laplacian eigenvalue of triangle-free graphs

Dongxiu Cai, Zhengbo Chen, Xiao-Dong Zhang

We prove that every finite simple triangle-free graph $G$ on $n \geq 1$ vertices satisfies $q_{m i n} (G) \leq 7 n /50$ , where $q_{m i n} (G)$ is the least eigenvalue of its signless Laplaci…

math.CO2026

A finite threshold for the double-comet conjecture

Dongxiu Cai, Zhenbo Chen, Xiao-Dong Zhang

For a tree $T$ , let $g (T) = λ_{1} (T) - λ_{2} (T)$ be the difference between its two largest adjacency eigenvalues. A balanced double comet is obtained by attaching equally many leaves to th…

math.CO2026

Polynomial positivity cones for Coxeter roots and walks in trees

Dongxiu Cai, Zhenbo Chen, Jiasheng Zeng +1

For a finite simple graph $G$ and an integer $k \geq 0$ , let $w_{k} (G)$ denote the number of walks of length $k$ . 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 $G$ of order $n$ and every $1 \leq k \leq n$ , $\sum_{i=…