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 ...

Extremal graph theory seeks to determine the maximum or minimum values of graph invariants—such as edge count, degree sequence or subgraph density—subject to the exclusion of particular configurations ...

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 ...

Graph labeling and colouring constitute a vibrant area of combinatorial mathematics concerned with the systematic assignment of discrete labels or colours to graph elements—typically vertices, edges ...

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 ...