Three Results for Trees, Using Mathematical Induction
نویسنده
چکیده
This paper presents three theorems each of which extends to trees a result that is known or obvious for a line segment. While the theorems are of interest in themselves, it is the purpose of the paper to use them as examples of how the inductive process may be effective in proving theorems for trees or for graphs with treelike structures. Other examples of the application of induction to trees include the proof that a tree with n nodes has n 1 arcs (cf. [5],· p. 35), or a paper such as [4]. The definition of a tree which will be used throughout is the followin g: A tree is a connected graph containing no cycles.
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