Question: this is a graph theory math question. thank you for your answer! Let T be a tree. Show (Without using Tutte's 1-factor theorem) that T

this is a graph theory math question. thank you for your answer!

Let T be a tree. Show (Without using Tutte's 1-factor theorem) that T has a perfect matching if and only if for every vertex v, exactly one of the components of T\\v has an odd number of vertices. [Hint for \"if\": use induction on |V(T)], nd a leaf With a neighbour of degree 2, and delete them both.]

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