What's up in

# Graph theory

## Latest Articles

### Four Is Not Enough

How many colors do you need to color an infinite plane so that no points 1 unit apart are the same color?

### First Big Steps Toward Proving the Unique Games Conjecture

The latest in a new series of proofs brings theoretical computer scientists within striking distance of one of the great conjectures of their discipline.

### Decades-Old Graph Problem Yields to Amateur Mathematician

By making the first progress on the “chromatic number of the plane” problem in over 60 years, an anti-aging pundit has achieved mathematical immortality.

### The Tricky Translation of Mathematical Ideas

Big advances in math can happen when mathematicians move ideas into areas where they seem like they shouldn’t belong.

### A Simple Visual Proof of a Powerful Idea

Ramsey’s theorem predicts a surprising (and useful) consistency in the organization of graphs. Here’s a simple visual proof of how it works.

### Graph Isomorphism Vanquished — Again

Just five days after posting a retraction, László Babai announced that he had fixed the error in his landmark graph isomorphism algorithm.

### Complexity Theory Problem Strikes Back

The legendary graph isomorphism problem may be harder than a 2015 result seemed to suggest.

### Landmark Algorithm Breaks 30-Year Impasse

Computer scientists are abuzz over a fast new algorithm for solving one of the central problems in the field.

### In Brain’s ‘Rich Club,’ Meetings of the Mind

Neuroscientists have identified a network of highly linked brain regions that could prove essential in integrating information and facilitating higher-order cognitive tasks.