Graph theory

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.

The “packing coloring” problem asks how many numbers are needed to fill an infinite grid so that identical numbers never get too close to one another. A new computer-assisted proof finds a surprisingly straightforward answer.

Unpredictability can help computer scientists solve otherwise intractable problems.

The four-color problem is simple to explain, but its complex proof continues to be both celebrated and despised.

Mathematicians have struggled to understand the moduli space of graphs. A new paper uses tools from physics to peek inside.

In Shang-Hua Teng’s work, theoretical and practical questions have long been intertwined. Now he’s turning his focus to the impractical.