Hong-xia Liu

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20222026

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4 papers · 1 filter

math.CO2026

The existence of odd-even factors in 1-binding graphs

Sizhong Zhou, Qiuxiang Bian, Hongxia Liu

Let $G$ be a graph. The binding number of $G$ , denoted by $\mbox{bind}(G)$, is defined as $$ \mbox{bind}(G)=\min\left\{\frac{|N_G(S)|}{|S|}:\emptyset\neq S\subseteq V(G) \ \mbox{an…

math.CO2026

Perfect matchings and $A_{α}$ -spectral radius in 1-binding graphs

Sizhong Zhou, Hongxia Liu

Let $G$ be a graph with vertex set $V (G)$ and edge set $E (G)$ . For $α \in [0, 1)$ , we use $A_{α} (G)$ and $ρ_{α} (G)$ to denote the $A_{α}$ -matrix and the $A_{α}$ -spectral radius of $G$ , respec…

math.CO2023

Some existence theorems on path-factor critical avoidable graphs

Sizhong Zhou, Hongxia Liu

A spanning subgraph $F$ of $G$ is called a path factor if every component of $F$ is a path of order at least 2. Let $k \geq 2$ be an integer. A $P_{\geq k}$ -factor of $G$ means a pat…

math.CO2022

Some sufficient conditions for path-factor uniform graphs

Sizhong Zhou, Zhiren Sun, Hongxia Liu

For a set $H$ of connected graphs, a spanning subgraph $H$ of $G$ is called an $H$ -factor of $G$ if each component of $H$ is isomorphic to an element of $\mathc…

The existence of odd-even factors in 1-binding graphs

Perfect matchings and Aα​-spectral radius in 1-binding graphs

Some existence theorems on path-factor critical avoidable graphs

Some sufficient conditions for path-factor uniform graphs

Perfect matchings and $A_{α}$ -spectral radius in 1-binding graphs