Graph reconfiguration and colouring problems investigate the transition between feasible solutions of a graph colouring instance. The central challenge is to determine a series of elementary vertex ...

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 ...

Have you ever tried to do the brainteaser below, where you have to connect the dots to make the outline of a house in one continuous stroke without going back over your lines? Or perhaps you've ...

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 ...

In the fall of 1972, Vance Faber was a new professor at the University of Colorado. When two influential mathematicians, Paul Erdős and László Lovász, came for a visit, Faber decided to host a tea ...