Abstract Forty years ago, Kleitman considered the numbers of crossings in good planar drawings of the complete bipartite graph ${K_{m,n}}$. Among other things, he ...

Coxeter theory investigates groups generated by reflections and the geometric structures arising from their actions, such as root systems and Dynkin diagrams. This body of work underpins vast areas of ...

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 ...

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 ...

We consider the bipartite matching model of customers and servers introduced by Caldentey, Kaplan and Weiss (2009). Customers and servers play symmetrical roles.There are finite sets C and S of ...

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 ...