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# graph theory

## Latest Articles

### A New Algorithm for Graph Crossings, Hiding in Plain Sight

Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory.

### When Math Gets Impossibly Hard

Mathematicians have long grappled with the reality that some problems just don’t have solutions.

### ‘Rainbows’ Are a Mathematician’s Best Friend

“Rainbow colorings” recently led to a new proof. It’s not the first time they’ve come in handy.

### Landmark Computer Science Proof Cascades Through Physics and Math

Computer scientists established a new boundary on computationally verifiable knowledge. In doing so, they solved major open problems in quantum mechanics and pure mathematics.

### Rainbow Proof Shows Graphs Have Uniform Parts

Mathematicians have proved that copies of smaller graphs can always be used to perfectly cover larger ones.

### The Map of Mathematics

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

### New Proof Settles How to Approximate Numbers Like Pi

The ancient Greeks wondered when “irrational” numbers can be approximated by fractions. By proving the longstanding Duffin-Schaeffer conjecture, two mathematicians have provided a complete answer.

### A 53-Year-Old Network Coloring Conjecture Is Disproved

In just three pages, a Russian mathematician has presented a better way to color certain types of networks than many experts thought possible.

### Computer Scientists Expand the Frontier of Verifiable Knowledge

The universe of problems that a computer can check has grown. The researchers’ secret ingredient? Quantum entanglement.