Math as a Liberal Art - Mathematics 105 - Fall 2008

A1. Explain why a graph that has an Euler non-closed path must have exactly two odd vertices.
A2: This problem is to help you see why Euler's Theorem works for connected graphs.

1. Give an example of a graph that's not connected, has no odd vertices, and has no Euler circuit.
2. Give an example of a graph that's not connected, has two odd vertices, and has no open Euler path.