PARTITIONING GRAPHS OF BOUNDED TREE-WIDTH

The paper discusses vertex partitions and edge partitions of graphs of bounded tree-width into graphs of smaller tree-width. The first part of the paper proves the existence of several kinds of such partitions. The second part, which has a Ramsey-theoretic character, shows that s ome of the results of the first part are close to being best possible. The last section of the paper presents a result on partitioning graph s of bounded tree-width into star-forests.