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, ...

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 ...

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 ...

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 ...

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 ...

Text: : "Graph Theory" by J. Adrian Bondy and U.S.R. Murty; Graduate Texts in Mathematics 244, Springer 2008. ISBN 978-1-84628-969-9, 2nd printing, 978-1-84628-970-5 (ebook). Notes will be supplied ...

In the natural selection theory, not a large number of mutant individuals appear at once, the mutation that "happens to the surrounding environment" happened by chance will spread over time throughout ...

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, ...

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 ...