Spanning Tree

A spanning tree of a connected undirected graph $G$ is a subgraph of it (every edge in the tree belongs to $G$) that spans $G$ (it includes every vertex of $G$).

Consider this graph:

Every tree below is a spanning tree of the graph above.

As can be seen above, a graph may have several spanning trees.

A spanning tree can be built by doing a BFS/DFS of the graph.

Recall the demo for BFS/DFS from prior chapters:

The spanning trees consist (only) of the thick edges.

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