Chapter 6.1, Problem 24MS

Path to proof. Suppose you have a connected graph in which every vertex has even degree except for two vertices with odd degree. If you add an edge between the two odd-degree vertices, what can you say about the resulting graph? Apply the reasoning from Mindscapes 22 and 23 to deduce that the original graph must have an Euler path that starts at one odd-degree vertex and ends at the other. Test your reasoning on graph (b) for Mindscape 20.