The study of graph colouring has long been a central topic in discrete mathematics, with a prominent focus on optimising the assignment of labels or colours to vertices such that adjacent vertices are ...

A k-graph is an ordered couple (V, E) where V is a set and E a set of k-tuples of elements of V; thus, a 2-graph is an ordinary graph. If the notions of the independent set and the chromatic number ...

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 ...

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, ...