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# Graph theory

## Latest Articles

### The Colorful Problem That Has Long Frustrated Mathematicians

The four-color problem is simple to explain, but its complex proof continues to be both celebrated and despised.

### Quantum Field Theory Pries Open Mathematical Puzzle

Mathematicians have struggled to understand the moduli space of graphs. A new paper uses tools from physics to peek inside.

### The Computer Scientist Who Finds Life Lessons in Games

In Shang-Hua Teng’s work, theoretical and practical questions have long been intertwined. Now he’s turning his focus to the impractical.

### Finally, a Fast Algorithm for Shortest Paths on Negative Graphs

Researchers can now find the shortest route through a network nearly as fast as theoretically possible, even when some steps can cancel out others.

### How Do You Prove a Secret?

Zero-knowledge proofs allow researchers to prove their knowledge without divulging the knowledge itself.

### Hypergraphs Reveal Solution to 50-Year-Old Problem

In 1973, Paul Erdős asked if it was possible to assemble sets of “triples” — three points on a graph — so that they abide by two seemingly incompatible rules. A new proof shows it can always be done.

### He Dropped Out to Become a Poet. Now He’s Won a Fields Medal.

June Huh wasn’t interested in mathematics until a chance encounter during his sixth year of college. Now his profound insights connecting combinatorics and geometry have led to math’s highest honor.

### Mathematical Connect-the-Dots Reveals How Structure Emerges

A new proof identifies precisely how large a mathematical graph must be before it contains a regular substructure.

### Researchers Achieve ‘Absurdly Fast’ Algorithm for Network Flow

Computer scientists can now solve a decades-old problem in practically the time it takes to write it down.