Question: 1. Can you trace over the entirety of Figure without lifting your writing instrument from the paper (or tracing any line twice)?
2. Given a graph with an Euler traversal but not circuit, how can you produce a graph with an Euler circuit?
3. Consider the complete graph Kn and any two vertices a and b in it.
(a) Why are there paths of every length from 1 to n-1 joining a and b?
(b) Find a graph other than K5 that has the property that there exist two vertices that have paths of lengths 1,2,...,4 joining them.
(c) While you're at it, find one for every n ≥ 4.