Hengzhe Li

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math.CO2024

Diameter two orientability of mixed graphs

Hengzhe Li, Zhiwei Ding, Jianbing Liu +1

In 1967, Katona and Szemerédi showed that no undirected graph with $n$ vertices and fewer than $\frac{n}{2} lo g_{2} \frac{n}{2}$ edges admits an orientation of diameter two. In 1978,…

math.CO2024

Characterization of Equimatchable Even-Regular Graphs

Xiao Zhao, Haojie Zheng, Fengming Dong +2

The study of equimatchable graphs traces back to Sumner (1979), followed by the foundational work of Lesk, Plummer, and Pulleyblank in 1984. Regarding the characterization of equim…

math.CO2024

A Note on Improved bounds for the Oriented Radius of Mixed Multigraphs

Hengzhe Li, Zhiwei Ding, Jianbing Liu +2

For a positive integer $r$ , let $f (r)$ denote the smallest number such that any 2-edge connected mixed graph with radius $r$ has an oriented radius of at most $f (r)$ . Recently, Bab…

math.CO2024

The $K_{1, 2}$ -structure-connectivity of graphs

Xiao Zhao, Haojie Zheng, Hengzhe Li

In this paper, we mainly investigate $K_{1, 2}$ -structure-connectivity for any connected graph. Let $G$ be a connected graph with $n$ vertices, we show that $κ (G; K_{1, 2})$ is well-…

Diameter two orientability of mixed graphs

Characterization of Equimatchable Even-Regular Graphs

A Note on Improved bounds for the Oriented Radius of Mixed Multigraphs

The K1,2​-structure-connectivity of graphs

The $K_{1, 2}$ -structure-connectivity of graphs