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# graph theory

## Latest Articles

### In Highly Connected Networks, There’s Always a Loop

Mathematicians show that graphs of a certain common type must contain a route that visits each point exactly once.

### To Pack Spheres Tightly, Mathematicians Throw Them at Random

Four mathematicians broke a 75-year-old record by finding a denser way to pack high-dimensional spheres.

### Topologists Tackle the Trouble With Poll Placement

Mathematicians are using topological abstractions to find places where it’s hard to vote.

### Maze Proof Establishes a ‘Backbone’ for Statistical Mechanics

Four mathematicians have estimated the chances that there’s a clear path through a random maze.

### The Year in Math

Landmark results in Ramsey theory and a remarkably simple aperiodic tile capped a year of mathematical delight and discovery.

### A Close-Up View Reveals the ‘Melting’ Point of an Infinite Graph

Just as ice melts to water, graphs undergo phase transitions. Two mathematicians showed that they can pinpoint such transitions by examining only local structure.

### New Proof Shows That ‘Expander’ Graphs Synchronize

The proof establishes new conditions that cause connected oscillators to sway in sync.

### Math That Lets You Think Locally but Act Globally

Knowing a little about the local connections on flight maps and other networks can reveal a lot about a system’s global structure.

### To Move Fast, Quantum Maze Solvers Must Forget the Past

Quantum algorithms can find their way out of mazes exponentially faster than classical ones, at the cost of forgetting the path they took. A new result suggests that the trade-off may be inevitable.