I was curious about graph theory and what prominent topics are involved in it. Perhaps one of the most interesting and practical problem I found in the Wikipedia entry for graph theory is the art gallery problem (also see here).
To sum it up: The problem asks us to consider how many security guards we’d need to carefully monitor an art gallery. This depends on many variables such as the size and shape of the art gallery.
Marianne Freiberger for Plus Magazine, summarizes the mathematician S. Fisk’s answer to this conundrum as:
..[Y]ou never need more than n/3 guards (so that’s 9/3 = 3 guards in the example in the figure). That’s true for any simple polygon with n vertices, no matter how complicated and irregular it looks.”
Which is pretty amazing.
So next time you’re watching your favorite heist movie or thinking about starting a heist campaign in D&D, consider the art gallery problem!