The Fastest Way yet to Color Graphs

Here’s a scary scenario: You’ve been put in charge of air traffic control at Newark airport near New York. You need to make sure every plane can taxi between the runway and its gate without hitting any other planes. Let’s bring the power of mathematics to bear on your problem. First, create a big, abstract map of your airport. For each runway, taxiway and gate, mark a point. Then, for each airplane, draw a line connecting these points: If a plane has to go from runway 4L down taxiway K to gate C80, draw a line that connects the points for runway 4L, taxiway K and gate C80. Now for the most important part: avoiding collisions. You’ll notice that every physical location has a lot of planes coming in and out of it — a lot of lines connected to every point on your map, which researchers call a graph. To ensure that no two planes are in the same place at the same time, you can color each of your lines and require that for every point, no two lines connected to it have the same color. The ... Read full article.