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 ...

Decades ago, Paul Erdős used randomness to illuminate the vast and weird world of networks. Now mathematicians are making his ...

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 ...

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 ...

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 ...