1)Prove that every simple not directed graph with 21 vertices and 208 edges has

a hamiltonian circuit but not an Euler circuit.

(I have proved that if we give the 2 edges for each vertices then after a few

steps I have 21 vertices of odd degree and 19 edges.So in the end I have 2

vertices of odd degree.So I have not an Euler circuit.But how can I prove that

there is a Hamiltonian one?)

2)If G is a tree and has a virtex k degree,prove that it also has at least k

vertices degree 1.