Graph theory

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

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

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

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

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

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.

A new result shows how much of the plane can be colored by points that are never exactly one unit apart.

Mathematicians can often figure out what happens as quantities grow infinitely large. What about when they are just a little big?

A new paper finds a faster method for determining when two mathematical groups are the same.