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 homomorphisms and chromatic numbers are foundational concepts in modern graph theory, with widespread applications that extend from combinatorial optimisation to theoretical computer science. 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 collection ...