1. Leaf is a vertex of degree one. Let T be a tree with 2n vertices in which no vertex has degree 2.

1. Leaf is a vertex of degree one. Let T be a tree with 2n vertices in which no vertex has degree 2. Show that T has at least n leaves.2. Give an example of an infinite tree which has paths of arbitrarily large finite length but no infinite path3. Construct all semi-Eulerian and semi-Hamiltonian trees on 100 vertices.4. Let T1,T2,T3 be subtrees of a finite tree T such that Ti ? Tj ?  {null} for all 1=2. Show that T has a path of length n-1.