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# graph theory

## Latest Articles

### Elegant Six-Page Proof Reveals the Emergence of Random Structure

Two young mathematicians have astonished their colleagues with a full proof of the Kahn-Kalai conjecture — a sweeping statement about how structure emerges in random sets and graphs.

### What a Math Party Game Tells Us About Graph Theory

Play this simple math game with your friends to gain insights into fundamental principles of graph theory.

### An Ancient Geometry Problem Falls to New Mathematical Techniques

Three mathematicians show, for the first time, how to form a square with the same area as a circle by cutting them into interchangeable pieces that can be visualized.

### Qubits Can Be as Safe as Bits, Researchers Show

A new result shows that quantum information can theoretically be protected from errors just as well as classical information can.

### Mathematicians Outwit Hidden Number Conspiracy

Decades ago, a mathematician posed a warmup problem for some of the most difficult questions about prime numbers. It turned out to be just as difficult to solve, until now.

### Researchers Defeat Randomness to Create Ideal Code

By carefully constructing a multidimensional and well-connected graph, a team of researchers has finally created a long-sought locally testable code that can immediately betray whether it’s been corrupted.

### How Big Data Carried Graph Theory Into New Dimensions

Researchers are turning to the mathematics of higher-order interactions to better model the complex connections within their data.

### Mathematicians Solve Decades-Old Classification Problem

A pair of researchers has shown that trying to classify groups of numbers called “torsion-free abelian groups” is as hard as it can possibly be.

### Mathematicians Answer Old Question About Odd Graphs

A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections.