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 ...

The local chromatic number of a graph G is the number of colors appearing in the most colorful closed neighborhood of a vertex minimized over all proper colorings of G. We show that two specific ...

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 ...