中文摘要：

图的划分问题是图论研究中最重要的一个问题之一，图论研究的很多问题都是特殊形式的划分问题，比如经典染色理论要求将图划分成最少的独立集，而最大k-部子图问题则是要找图中边数最多的一个k-部子图．本文给出划分问题的一些最新进展，以及一些尚未解决的问题，其中大部分是来自于求最大k-部子图的相关领域．

英文摘要：

Graph partition problem is one of the most important topics in structural graph theory, since many problems in graph theory can be treated as a partition of the vertices into sets with some properties. For instance, the classical vertex coloring problem asks for a partition into minimum number of independent sets, and the maximum k-partite subgraph problem asks for a k-partite subgraph with maximum number of edges. In this paper, we present some results and problems on graph partitions, of which most are from the topic originated from the maximum k-partite subgraph problem.