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 ...

Gallai–Ramsey theory lies at the intersection of graph colouring and Ramsey theory, providing a framework for understanding how structures emerge in edge-coloured graphs. Central to this domain is the ...

In geography it is important to be able to read and understand data that is presented in a range of different ways. We often use graphs to present data in a clear and accessible way. There are many ...

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 ...

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 ...

Back in the hazy olden days of the pre-2000s, navigating between two locations generally required someone to whip out a paper map and painstakingly figure out the most optimal route between those ...

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 ...