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# graph theory

## Latest Articles

### 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.

### 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.