My latest column for *Quanta Magazine* explores some recent results in graph theory that use local information to draw global conclusions, a powerful tool in math! It begins with a puzzle.

In math, as in life, small choices can have big consequences. This is especially true in graph theory, a field that studies networks of objects and the connections between them. Here’s a little puzzle to help you see why.

Given six dots, your goal is to connect them to each other with line segments so that there’s always a path between any pair of dots, with no path exceeding two line segments in length.

You can see the solution to the puzzle and learn how it connects to new results in graph theory by reading the full article here for free.