An edge-colored graph G is conflict-free connected if any two of its vertices are connected by a path, which contains a color used on exactly one of its edges. The conflict-free connection number of a connected graph G, denoted by cfc(G), is defined as the minimum number of colors that are required in order to make G conflict-free connected. In this paper, we investigate the relation between the conflict-free connection number and the independence number of a graph. We firstly show that cfc(G) ≤ α(G) for any connected graph G, and give an example to show that the bound is sharp. With this result, we prove that if T is a tree with \(\Delta(T)\geq\frac{\alpha(T)+2}{2}\), then cfc(T) = Δ(T).

如果边缘着色图形G的任意两个顶点通过一条路径连接，则该边缘着色图形G是无冲突的，该路径包含恰好在其边缘之一上使用的颜色。连通图G的无冲突连接数（用cfc（G）表示）定义为使G无冲突地连接所需的最小颜色数。在本文中，我们研究了无冲突连接数与图的独立数之间的关系。我们首先表明，CFC（ģ）≤ α（ģ）对于任何连通图G ^，并举例说明边界是尖锐的。以此结果证明，如果T是具有\（\ Delta（T）\ geq \ frac {\ alpha（T）+2} {2} \）的树，则cfc（T）=Δ（T）。