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Chinese Postman Problem -- Too Simple?

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I have been exploring the chinese postman problem, and I'm really worried that it's too simple/there aren't enough mathematics involved. I explained the problem, gave a couple of examples, but there isn't much calculus/numerical calculations. In general, it only really consists of graph theory. My teacher recommended that I add in permutations, maybe probability, but I have little to no idea how I can accomplish that. 

I was considering using permutations to explore how many directed graphs can be made of the undirected graph; however, this has been classified as np-hard and is likely a dead-end. I also considered using pascal's grid to find the pathways, but CPP requires the return to the initial vertice, so that is not possible. Do you guys have any idea how I could include more math in my IA?

 

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