Graph polynomials serve as robust algebraic encodings of the intricate combinatorial properties inherent to graphs. At the heart of this discipline lies the Tutte polynomial, an invariant that not ...

Chemical graph theory provides a rigorous framework for representing molecular structures as graphs, where vertices denote atoms and edges represent bonds. This mathematical abstraction facilitates ...

Jacob Holm was flipping through proofs from an October 2019 research paper he and colleague Eva Rotenberg—an associate professor in the department of applied mathematics and computer science at the ...

Researchers have proved a special case of the Erdős-Hajnal conjecture, which shows what happens in graphs that exclude anything resembling a pentagon. When you walk into a room full of people, you can ...

The original version of this story appeared in Quanta Magazine. Much of mathematics is driven by intuition, by a deep-rooted sense of what should be true. But sometimes instinct can lead a ...

Much of mathematics is driven by intuition, by a deep-rooted sense of what should be true. But sometimes instinct can lead a mathematician astray. Early evidence might not represent the bigger picture ...