Graph theory is a discipline that seems to get more important every day. It maps relationships between objects, and that has lots of practical uses. Graph theory is what determines your postal delivery worker’s most efficient route through a series of neighborhoods. It’s what tracks the spread of public health crises and undergirds every social media platform on the internet.
But one of the simplest problems in mathematics -- how to connect three utilities to three houses without crossing lines -- has proven to be impossible. Grab a sheet of paper and try it out. It won’t take long to realize you can get very close, but never solve the three utilities problem -- and you’ll see quickly that graph theory is a hidden force in everyday life.
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