In the field of graph theory, specifically in chemical graph theory, a chemical molecule is represented by a molecular graph, which is a simple graph. In this representation, vertices denote the atoms ...

Network science has become a powerful tool to describe the structure and dynamics of real-world complex physical, biological, social, and technological systems. Largely built on empirical observations ...

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. “There is no absolute randomness in ...

Keep Learning is available to stream on pbs.org and the free PBS App, available on iPhone, Apple TV, Android TV, Android smartphones, Amazon Fire TV, Amazon Fire Tablet, Roku, Samsung Smart TV, LG TV, ...

The original version of this story appeared in Quanta Magazine. All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in ...

Now that pandemic restrictions are easing up, people are getting together again. But it’s been a while, so if you and your friends need some help breaking the ice, here’s a mathematical party game you ...

Sure, you can cut a pie into pieces, but what if it’s in four dimensions? Using spectral graph theory, mathematicians have solved a decades-old problem. Graph theory uses nodes and edges (dots and ...