中文摘要：

设k≥2是一个整数。本文证明了任意有m条边的图都存在一个顶点的划分V_1,V_2…,V_k,使得e（V_1,V_2…,V_k）≥k-1/k m＋k-1/2k（（2m＋1/4）~1/2-1/2）-（k-2）~2/8k,且max{e（V_i）：1≤i≤k}≤m/k~2＋（k-1）/2k~2（（2m＋1/4）~1/2-1/2＋3/8-7k-4/8k~2.我们的结果改进了[Fan G.,Hou J.,Zeng Q.,A bound for judicious k-partitions of graphs,Discrete Appl.Math.,2014,179：86—99]的主要结论.

英文摘要：

Suppose thatk≥2 is an integer. In this note, we prove that every graphwith m edges admits a partition V1, V2,... Vksuch that e（V_1,V_2…,V_k）≥k-1/k m＋k-1/2k（（2m＋1/4）~1/2-1/2）-（k-2）~2/8k This improves the main result of [Fan G., Hou J., Zeng Q., A bound forjudicious k-partitions of graphs, Discrete Appl. Math., 2014, 179： 86-99].