Zhiyu Wang

activity

20232025

collaborators

5 papers

math.CO2025

Counting $k$ -cycles in $5$ -connected planar triangulations

Gyaneshwar Agrahari, Xiaonan Liu, Zhiyu Wang

We show that every $n$ -vertex $5$ -connected planar triangulation has at most $9 n - 50$ many cycles of length $5$ for all $n \geq 20$ and this upper bound is tight. We also show that fo…

math.CO2025

On the smallest eigenvalues of $3$ -colorable graphs

Zilin Jiang, Zhiyu Wang

We prove that the set of the smallest eigenvalues attained by $3$ -colorable graphs is dense in $(- \infty, - λ^{*})$ , where $λ^{*} = ρ^{1/2} + ρ^{- 1/2} \approx 2.01980$ and $ρ$ is the po…

math.CO2024

On the oriented diameter of graphs with given minimum degree

Garner Cochran, Zhiyu Wang

Erdős, Pach, Pollack, and Tuza [\textit{J. Combin. Theory Ser. B, 47(1) (1989), 73-79}] proved that the diameter of a connected $n$ -vertex graph with minimum degree $δ$ is at most…

math.CO2024

On tight $(k, ℓ)$ -stable graphs

Xiaonan Liu, Zi-Xia Song, Zhiyu Wang

For integers $k > ℓ \geq 0$ , a graph $G$ is $(k, ℓ)$ -stable if $α (G - S) \geq α (G) - ℓ$ for every $S \subseteq V (G)$ with $∣ S ∣ = k$ . A recent result of Dong and Wu [SIAM J. Discrete Mat…

math.CO2023

On the oriented diameter of near planar triangulations

Yiwei Ge, Xiaonan Liu, Zhiyu Wang

In this paper, we show that the oriented diameter of any $n$ -vertex $2$ -connected near triangulation is at most $⌈ \frac{n}{2} ⌉$ (except for seven small exceptions), and…

Counting k-cycles in 5-connected planar triangulations

On the smallest eigenvalues of 3-colorable graphs

On the oriented diameter of graphs with given minimum degree

On tight (k,ℓ)-stable graphs

On the oriented diameter of near planar triangulations

Counting $k$ -cycles in $5$ -connected planar triangulations

On the smallest eigenvalues of $3$ -colorable graphs

On tight $(k, ℓ)$ -stable graphs