Suppose G is a connected graph and T is a circuitfree subgraph of G. Suppose also that if any edge e of G not in T is added to T, the resulting graph contains a circuit. Prove that T is a spanning tree for G.
The proof of the given statement about spanning tree.
A proposition is given as,
Suppose is a connected graph and is a circuit free subgraph of . Suppose also that if any edge of not in is added to the resulting graph contains a circuit. Prove that is a spanning tree for .
There can be two cases for the given subgraph either it is connected, or it is disconnected.
According to the given information the given subgraph is circuit free and we have assumed that it is connected so all vertices are reachable
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