Semi-Eulerization Algorithm (for dummies)

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I'm an engineer by training, not a CS person, so this question may come across as rather simplistic, but hopefully someone can give me some help.

I've got a graph that is non-Eulerian, but needs to be traced by an Eulerian path (not an Eulerian tour, hopefully). In order to semi-Eulerize it, I can only remove edges. What I want to figure out is how to do this with removing the fewest number of edges possible.

How would I construct an algorithm to do this? Ideally, a step-by-step description would be great. (remember: engineer, not CS person ... sorry)

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