Graph colouring is a fundamental problem in both theoretical and applied combinatorics, with significant implications for computer science, operational research and network theory. At its essence, ...

Graph labeling is a central topic in combinatorial optimisation that involves assigning numerical or categorical labels to vertices or edges of a graph subject to specific constraints. This framework ...

In just three pages, a Russian mathematician has presented a better way to color certain types of networks than many experts thought possible. A paper posted online last month has disproved a ...

In 1950 Edward Nelson, then a student at the University of Chicago, asked the kind of deceptively simple question that can give mathematicians fits for decades. Imagine, he said, a graph — a ...

Four years ago, the mathematician Maria Chudnovsky faced an all-too-common predicament: how to seat 120 wedding guests, some of whom did not get along, at a dozen or so conflict-free tables. Luckily, ...