I have to find an upper bound for vertices of degree one in a tree which has n vertices. I think it would be n-1 - we can always form a tree with one vertice in its center and the other ones are connected only with the centre, so we get n-1 vertices of degree one and one of degree n-1. I don't know how to prove this or if my idea is ok.
2026-03-28 15:11:57.1774710717
Upper bound for vertices of degree one in a tree
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Since there is $n$ vertices and they can not have all degree $1$ (else all of them would be in pairs making $n/2$ components and would be disconected) your example show that max is $n-1$.