AI 中文总结
本文针对图的无冲突连接数问题，提出了保证该参数有界的4个独立顶点最小度和的尖锐条件。
AI 中文摘要
边染色图中的一条路径被称为无冲突路径，若其颜色仅应用于该路径的一条边。图G被称为无冲突连通，若V(G)中的每对顶点都由一条无冲突路径连接。将连通图G染为无冲突连通所需的最少颜色数称为无冲突连接数。本文针对G中任意4个独立顶点的最小度和，引入若干尖锐条件，以确保G的无冲突连接数有界。
英文摘要
A path in an edge-coloured graph is called \emph{conflict-free} if a colour is exclusively applied to one of its edges. A graph $G$ is considered \emph{conflict-free connected} if every pair of vertices in $V(G)$ is connected by a conflict-free path. The minimum number of colours required to render a connected graph $G$ conflict-free connected is referred to as the \emph{conflict-free connection number}. In this paper, we introduce several sharp conditions on the minimum degree sum of any $4$ independent vertices in $G$ to ensure that the conflict-free connection number of $G$ is bounded.
Comments20 pages
