Rui-Fang Liu

activity

20232026

collaborators

8 papers

math.CO2026

Spectral extremal problems on $[a, b]$ -factors in binding graphs, and beyond

Ting Xu, Ruifang Liu

The binding number $b (G)$ of a graph $G$ is the minimum value of $∣ N_{G} (X) ∣/∣ X ∣$ taken over all nonempty sets $X \subseteq V (G)$ such that $N_{G} (X) \neq = V (G)$ . A graph $G$ is 1-bin…

math.CO2026

Extremal results for graphs with binding number strictly less than $1/ r$

Ruifang Liu, Hongyu Chen, Ao Fan

The binding number $b (G)$ of a graph, introduced by Woodall [J. Combin. Theory, Ser. B, 1973], is a central topic of both structural and extremal graph theory. It is closely relate…

math.CO2026

Spectral radius and rainbow $k$ -factors in a bipartite graph family

Meng Chen, Ruifang Liu

Let $G = {G_{1}, G_{2}, \dots, G_{k n}}$ be a family of balanced bipartite graphs on the same vertex set $[2 n]$ . A rainbow $k$ -factor of $G$ is defined as a $k$ -fa…

math.CO2026

Spectral radius and rainbow Hamiltonicity in bipartite graphs

Meng chen, Ruifang Liu, Qixuan Yuan

Let $G = {G_{1}, G_{2}, \dots, G_{k}}$ be a family of bipartite graphs on the same vertex set. A rainbow Hamilton path (cycle) in $G$ is a path (cycle) that visits…

math.CO2026

Spectral radius and parity $[a, b]$ -factors in graphs

Ruifang Liu, Ting Xu, Suil O

Let $a$ , $b$ , and $n$ be three integers such that $1 \leq a \leq b < n$ , $a \equiv b$ (mod $2$ ), and $na$ is even. A parity $[a, b]$ -factor of $G$ is a spanning subgraph $H$ such tha…

math.CO2025

Toughness in regular graphs from eigenvalues

Ruifang Liu, Ao Fan, Jinlong Shu

The {\it toughness} $τ(G)=\mathrm{min}\{\frac{|S|}{c(G-S)}: S~\mbox{is a vertex cut in}~G\}$ for $G ≆ K_{n},$ which was initially proposed by Chvátal in 1973. A graph $G$ is call…

math.CO2025

Turán number of books in non-bipartite graphs

Lu Miao, Ruifang Liu, Edwin R. van Dam

Let $ex (n, H)$ be the Turán number of $H$ for a given graph $H$ . A graph is color-critical if it contains an edge whose removal reduces its chromatic number. Simonovits' c…

math.CO2023

Toughness and distance spectral radius in graphs involving minimum degree

Jing Lou, Ruifang Liu, Jinlong Shu

The toughness $τ(G)=\mathrm{min}\{\frac{|S|}{c(G-S)}: S~\mbox{is a cut set of vertices in}~G\}$ for $G ≆ K_{n} .$ The concept of toughness initially proposed by Chv$\mathrm{\acute…

Spectral extremal problems on [a,b]-factors in binding graphs, and beyond

Extremal results for graphs with binding number strictly less than 1/r

Spectral radius and rainbow k-factors in a bipartite graph family

Spectral radius and rainbow Hamiltonicity in bipartite graphs

Spectral radius and parity [a,b]-factors in graphs

Toughness in regular graphs from eigenvalues

Turán number of books in non-bipartite graphs

Toughness and distance spectral radius in graphs involving minimum degree

Spectral extremal problems on $[a, b]$ -factors in binding graphs, and beyond

Extremal results for graphs with binding number strictly less than $1/ r$

Spectral radius and rainbow $k$ -factors in a bipartite graph family

Spectral radius and parity $[a, b]$ -factors in graphs