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Section 16.5 Spanning trees
spanning subgraph
a subgraph that contains all the vertices of the parent graph
spanning tree
a spanning subgraph that is a tree
Example 16.5.1 . Spanning trees for the complete graph \(K_4\) .
Here is the complete graph with four vertices.
And here are ten different spanning trees for \(K_4\text{.}\)
If we carry out either of the depth-first or breadth-first search algorithms, but aren’t looking for a path between specific vertices, the end result will be a spanning tree for the original graph.
depth-first spanning tree
the result of performing the depth-first search algorithm on a graph, continuing until all vertices in the original graph appear in the search tree
breadth-first spanning tree
the result of performing the breadth-first search algorithm on a graph, continuing until all vertices in the original graph appear in the search tree
Example 16.5.2 . Depth-first and breadth-first spanning trees.
Figure 16.5.3. Examples of depth- and breadth-first spanning trees.
