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 ...

Deep in the heart of Microsoft, Jennifer Chayes and Christian Borgs lead a who's who of mathematics and computer science. The goal? To explore anything they please Every weekday afternoon some 20 ...

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 ...

Anti-Ramsey theory in graphs is a branch of combinatorial mathematics that examines the conditions under which a graph, when its edges are coloured, must necessarily contain a ‘rainbow’ subgraph – a ...

Researchers thought that they were five years away from solving a math riddle from the 1980's. In reality, and without knowing, they had nearly cracked the problem and had just given away much of 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 ...