Commutative algebra and graph theory are two vibrant areas of mathematics that have grown increasingly interrelated. At this interface, algebraic methods are applied to study combinatorial structures, ...

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 ...

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 ...

In math, as in life, small choices can have big consequences. This is especially true in graph theory, a field that studies networks of objects and the connections between them. Here’s a little puzzle ...

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 ...

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 ...

Let’s say you’re planning your next party and agonizing over the guest list. To whom should you send invitations? What combination of friends and strangers is the right mix? It turns out ...

A survey of contemporary topics in mathematics such as: voting systems and power, apportionment, fair division of divisible and indivisible assets, efficient distribution, scheduling and routing, ...