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, ...

It is shown that for arbitrary positive integers $m, n$ there exists a $\phi(m, n)$ such that if $\chi(G) \geqslant \phi(m, n)$, then $G$ contains either a complete ...

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 ...