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Math Trek

The four color problem gets a sharp new hue

Mathematicians find new answers to the still puzzling theorem that four colors suffice to color any map.

3:27pm, March 6, 2009

In 1852, botanist Francis Guthrie noticed something peculiar as he was coloring a map of counties in England. Despite the counties’ meandering shapes and varied configurations, four colors were all he needed to shade the map so that any two bordering counties were different colors. Perhaps, he speculated, four colors were enough for any map.

Little did Guthrie know the load of trouble he unleashed with his innocent conjecture. It took mathematicians nearly a century and a quarter to prove him right, and even that wasn’t enough to close the Pandora’s box Guthrie had opened. Mathematicians pulled out their markers and tried to color everything in sight.

The particular things mathematicians wanted to color were graphs: dots connected by lines Such graphs can be used to describe everything from friendships to the Internet to gene interactions. They can even describe maps, if the countries correspond to dots and bordering countries are connected by line

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