Bootstrap percolation, a model of irreversible activation on graphs, has emerged as a pivotal area within graph theory and statistical mechanics. In this process, nodes (or vertices) on a network are ...

The study of geodetic numbers in graph theory represents a compelling fusion of abstract mathematical ideas with practical applications across network analysis, computational optimisation, and ...

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 ...

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 ...