Tight Cuts

In Chapter 2 we introduced the operation of splicing which can be used to ‘combine’ two matching covered graphs to obtain another matching covered graph. Here we introduce the related notion of a separating cutwhich leads to away of ‘decomposing’ a matching covered graph into two matching covered graphs. Tight cuts are a special type of separating cuts. They play a pivotal role in many aspects of this theory, including the study of questions concerning the existence of an edge in a matching covered graph whose deletion results in another matching covered graph.