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 ...

Graph theory has long provided a robust mathematical framework for investigating networks, relations and connectivity in both abstract and applied settings. Recent advances have markedly refined our ...

Graph theory isn’t enough. The mathematical language for talking about connections, which usually depends on networks—vertices (dots) and edges (lines connecting them)—has been an invaluable way to ...

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 ...

It has been an exhilarating year in combinatorics research. In early 2023, mathematicians were stunned when two of the biggest problems in the field were solved in as many months. Now, a third major ...

Like many of us, [Tim]’s seen online videos of circuit sculptures containing illuminated LED filaments. Unlike most of us, however, he went a step further by using graph theory to design glowing ...