I am having difficulties with this problem.
Let T be a tree with k leaves and set [tex]t=ceiling(k/2)/MATH]. Prove that there exists paths which satisfy the following
ii) for every i<j.
EDIT: going over my work i realized that my proof doesn't hold. So I'd appreciate any help on where to start. Induction seems to be the natural choice but i can't get it to work for any parameter.