Explaination of Graph Theory concept

Question

Can anyone please let me know the proof or intuition behind the statement given below? "Given the connected graph, if you take any one of the spanning tree then remaining part of graph is bipartite"

Answer 1

The statement as it is now is false: Take $K_5$ for example.

Let the vertices be $v_1, v_2, v_3, v_4, v_5$ and the chosen spanning tree to be the path $v_1 - v_2 - v_3 - v_4 - v_5$.

Then in the complement we have an odd cycle $v_1 - v_3 - v_5 - v_2 - v_4 - v_1$ hence the new graph can't be bipartite.