I'm completing a graph theory assignment, and one of the problems states,
Prove that a tree $T$ has a perfect matching if and only if $o(T-v) = 1$ for every $v \in V (T)$.
I'm not asking for help answering this question, but rather for help understanding the notation. What does $o(G)$ usually mean in graph theory? If it has multiple conventional meanings, which are the most common?
One thought I had was that it could be the number of odd disconnected components left after removing some vertices, but I believe that following that definition's implications has lead me to a disproof of the statement in the question, so I don't think that's correct.