Suppose that T_1 and T_2 are spanning trees of a simple graph G. Moreo

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Module 5: Graphs and Trees

20225m

Suppose that $T_1$ and $T_2$ are spanning trees of a simple graph $G$ . Moreover, suppose that $e_1$ is an edge in $T_1$ that is not in $T_2$ . Show that there is an edge $e_2$ in $T_2$ that is not in $T_1$ such that $T_1$ remains a spanning tree if $e_1$ is removed from it and $e_2$ is added to it, and $T_2$ remains a spanning tree if $e_2$ is removed from it and $e_1$ is added to it.

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