Component Factors and Connected Factors

Graph factor problems have been studied extensively for many years. Most of the results mentioned in the previous chapters are of type “degree constraint factors”, i.e., finding a spanning subgraph with given degree conditions. Many of these “degree constraint factors” problems can be transformed to matching problems, and therefore there exist efficient algorithms to determine it. However, there is another type of factor problem, generally referred as “component factor problem”, which consider a spanning subgraph with components isomorphic to the members of a given list. In this chapter, we discuss the component factors and connected factors. There exist characterizations for a few of these problems, but for most cases characterizations have not been discovered yet.