[yomly]

Isn't changing the problem usually quite an elegant way to solving a problem..? I don't have any examples to hand, but I'm pretty sure being able to rerepresent or slightly change a problem has been applied to great success. In the applied sciences at least...

[raverbashing]

Yes

For theoretical problems sure, you want to solve that problem, though a lot of solutions rely on analyzing a partial graph with some edges removed

For practical problems, changing the problem might be much cheaper/easier than keeping to the original one

[perfmode]

In the article:

> We take all the destinations that have an odd number of connections in this tree (Euler proved there must be an even number of these), and carefully pair them up. Because all the destinations now have an even number of edges, we’ve created an Eulerian graph, so we create a route that crosses each edge exactly once.