Let \(\mathrm{pr}(K_{n}, G)\) be the maximum number of colors in an edge-coloring of \(K_{n}\) with no properly colored copy of G. For a family \({\mathcal {F}}\) of graphs, let \(\mathrm{ex}(n, {\mathcal {F}})\) be the maximum number of edges in a graph G on n vertices which does not contain any graphs in \({\mathcal {F}}\) as subgraphs. In this paper, we show that \(\mathrm{pr}(K_{n}, G)-\mathrm{ex}(n, \mathcal {G'})=o(n^{2}), \) where \(\mathcal {G'}=\{G-M: M \text { is a matching of }G\}\). Furthermore, we determine the value of \(\mathrm{pr}(K_{n}, P_{l})\) for sufficiently large n and the exact value of \(\mathrm{pr}(K_{n}, G)\), where G is \(C_{5}, C_{6}\) and \(K_{4}^{-}\), respectively. Also, we give an upper bound and a lower bound of \(\mathrm{pr}(K_{n}, K_{2,3})\).

设\(\mathrm{pr}(K_{n}, G)\)是\(K_{n}\)的边缘着色中的最大颜色数，没有G 的正确着色副本。对于一系列\({\mathcal {F}}\)图，令\(\mathrm{ex}(n, {\mathcal {F}})\)是图G在n上的最大边数\({\mathcal {F}}\)中不包含任何图的顶点作为子图。在本文中，我们证明\(\mathrm{pr}(K_{n}, G)-\mathrm{ex}(n, \mathcal {G'})=o(n^{2}), \)其中\(\mathcal {G'}=\{GM: M \text { 是 }G\}\) 的匹配。此外，我们确定\(\mathrm{pr}(K_{n}, P_{l})\) 的值对于足够大的n和\(\mathrm{pr}(K_{n}, G)\)的精确值，其中G是\(C_{5}, C_{6}\)和\(K_{4} ^{-}\)，分别。此外，我们给出了\(\mathrm{pr}(K_{n}, K_{2,3})\)的上限和下限。