A tree is a connected undirected graph with no cycles.

It is a spanning tree of a graph G if it spans G (that is, it *includes every vertex of G*) and is a subgraph of G (every edge in the tree belongs to G).

A spanning tree of a connected graph G can also be defined as a maximal set of edges of G that contains no cycle or as a minimal set of edges that connect all vertices.

https://en.wikipedia.org/wiki/Spanning_tree

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