Topic: circuit list of topics
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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.
	The two-digit numbers from 10-99		1998-01-21
		From Alexis Riddle: My name is Alexis. I'm a student in 8th grade and I'm taking Algebra I Honors. My question is: In a string of numbers, two adjacent digits are considered as a two-digit number. For instance, the string 11012 contains the numbers 10, 11, and 12. What is the number of digits in the smallest string that contains all of the two-digit numbers from 10-99? Please help and thank you for any assistance you can give me. Answered by Penny Nom.

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