Yes, there always exists such a path, but it necessarily begins on one of the vertices with odd degree and necessarily ends up on the other. Graphs with more than two vertices with odd degree. No, a path is never possible no matter it begins. Euler generalized his analysis of the 7 Bridges problem even further, into both the domain of graph theory, and that of what we now call topology. Having seen a few examples of mathematical statements and mathematical proof, consider the following statements drawn from various walks of life.
All bachelors are unmarried males.
The earth revolves around the sun. In the criminal justice system of the United States, a defendant is presumed to be innocent until he or she is proven guilty. Albany is the capital of New York State. The square-root of 5 is an irrational number . Table salt is a combination of sodium and chlorine.