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A hamiltonian circuit 2006-07-24
From Tom:

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.

Answered by Penny Nom.



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