Kun Cheng

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20242026

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math.CO2024

Constructions of minimally $t$ -tough regular graphs

Kun Cheng, Chengli Li, Feng Liu

A non-complete graph $G$ is said to be $t$ -tough if for every vertex cut $S$ of $G$ , the ratio of $∣ S ∣$ to the number of components of $G - S$ is at least $t$ . The toughness $τ (G)$ o…

math.CO2024

Sparse graphs with an independent or foresty minimum vertex cut

Kun Cheng, Yurui Tang, Xingzhi Zhan

A connected graph is called fragile if it contains an independent vertex cut. In 2002 Chen and Yu proved that every connected graph of order $n$ and size at most $2 n - 4$ is fragile,…

Constructions of minimally t-tough regular graphs

Sparse graphs with an independent or foresty minimum vertex cut

Constructions of minimally $t$ -tough regular graphs