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# graph theory

## Latest Articles

### 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.

### New Proof Reveals That Graphs With No Pentagons Are Fundamentally Different

Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon.

### Mathematicians Settle Erdős Coloring Conjecture

Fifty years ago, Paul Erdős and two other mathematicians came up with a graph theory problem that they thought they might solve on the spot. A team of mathematicians has finally settled it.

### Pioneers Linking Math and Computer Science Win the Abel Prize

Avi Wigderson and László Lovász won for their work developing complexity theory and graph theory, respectively, and for connecting the two fields.

### Undergraduate Math Student Pushes Frontier of Graph Theory

At 21, Ashwin Sah has produced a body of work that senior mathematicians say is nearly unprecedented for a college student.

### Disorder Persists in Larger Graphs, New Math Proof Finds

David Conlon and Asaf Ferber have raised the lower bound for multicolor “Ramsey numbers,” which quantify how big graphs can get before patterns inevitably emerge.