To probe an unexplored space of hard problems, researchers play the devil's advocate

In computer science, the graph coloring problem is a classic. Inspired by the map-coloring problem, it asks: Given a network of nodes connected by links, what’s the minimum number of colors you need to color each node so that no links connect two of the same color? For small numbers of colors and links, looking for a solution is straightforward: Just try all possible combinations. But as links increase, the problem becomes more constrained—until, if there are too many links and not enough colors, no solution may exist at all.

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