16: Trees and searches Last updated Save as PDF Page ID 83482 Jeremy Sylvestre University of Alberta Augustana 16.1: Motivation Reducing redundancy. You have set up your own tree-fort communication system out of tin cans and strings. 16.2: Basics Trivial Path: a path that consists of a single vertex 16.3: Identifying Trees Theorem: Characterizations of trees. The following are equivalent for a graph G=(V,E) with |V|=n vertices. 16.4: Depth-first and breadth-first searches Let G be a graph. Given vertices v,v′ of G, we might wish to find a path from v to v′, if one exists. We can do this by constructing a tree T⪯G. 16.5: Spanning Trees Spanning Subgraph: a subgraph that contains all the vertices of the parent graph 16.6: Binary Searches Binary Search Tree: a tree in which every node has degree 1 or 3, except for a single node of degree 2. 16.7: Activities 16.8: Exercises