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graph theory

Illustration for "Four Is Not Enough"
Quantized Academy

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?

Lede art for "First Big Steps Toward Proving the Unique Games Conjecture"
computational complexity

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.

Illustration of 826-vertex graph for "Decades-Old Graph Problem Yields to Amateur Mathematician"
graph theory

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.

Graph
Abstractions blog

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.

Abstractions blog

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.

Illustration: boxing gloves
Abstractions blog

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.

Illustration: boxing glove & graph
Abstractions blog

Complexity Theory Problem Strikes Back

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

Computer Science

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.

neuroscience

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.