Graph coloring problems are widely applicable to the problem of scheduling.
Consider a University, where you are trying to schedule times for all of the final exams. Some students are taking more than one class, so you want to make sure they don't have two exams scheduled at the same time. However, you want your exam writing period to be as short as possible, to run as many exams concurrently as you can.
You can represent this as a Graph coloring problem: you make $G=(V,E)$ where each class is a vertex, and an edge between vertices any time a two classes contain the same student. Your colors will represent different exam timeslots. The minimum number with which you can color that graph is the smallest number of timeslots you need to write all your exams.
The problem in general is NP hard, but if you had some knowledge about your schedule, say, that it was planar, then you could apply the 4-color theorem to write all of the exams together.
I'm not 100% certain you'd ever get a planar graph in a real-life scheduling problem, but there's a wider lesson here: graphs are widely applicable to things which aren't immediately obvious. The 4-color theorem isn't just about graphs and maps, it can be used to model real life problems where you're expressing some set of objects, and some binary relations between those objects.