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 ...

A theorem for coloring a large class of “perfect” mathematical networks could ease the way for a long-sought general coloring proof. Four years ago, the mathematician Maria Chudnovsky faced an all-too ...

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 ...