ABSTRACT
There is one simple and important kind of graph which has been given the same name by all authors, namely a tree. Trees are important not only for sake of their applications to many different fields, but also to graph theory itself. One reason for the latter is that the very simplicity of trees make it possible to investigate conjectures for graphs in general by first studying the situation for trees. Several ways of defining a tree are developed. The chapter discusses a tree which is naturally associated with every connected graph: its block-cutpoint tree. Using geometric terminology, it explains centrality of trees. A tree is a connected acyclic graph. Any graph without cycles is a forest, thus the components of a forest are trees. It has often been observed that a connected graph with many cutpoints bears a resemblance to a tree.
