关于图的单圈划分

Unicycle Partition of A Graph

图的划分问题曾引起图论界的广泛关注 ,本文讨论了一般的单圈划分问题 ,利用禁用构形刻划了一个图存在单圈划分的条件 ,并进一步得到一个算法 ,有效地解决了判定一个图是否存在单圈划分 ,若存在则求其单圈划分的问题 .

The problem of partitioning a graph has been long concerned. We discuss the general unicycle partition problem in this paper. By way of forbidden configurations, it is characterized when a graph has a unicycle partition. Furthermore, an efficient algorithm is reached to decide whether a unicycle partition of a graph exists or not, and if it exists, we can get it.