Graph theory

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.

Mathematicians probe the limits of randomness in new work estimating quantities called Ramsey numbers.

By treating molecules as geometric tessellations, scientists devised a new way to forecast how 2D materials might self-assemble.

New tools make it possible to detect hidden manipulation of maps.

Four mathematicians have found a new upper limit to the “Ramsey number,” a crucial property describing unavoidable structure in graphs.