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 graph colouring problem, a classic NP-hard challenge, is central to many practical applications such as scheduling, resource allocation and network management. Recent advances have seen the ...

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 ...

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 ...

One of the great episodes in the history of mathematics began on October 23, 1852. In a letter to Sir William Rowan Hamilton, Augustus De Morgan wrote, “A student of mine asked me today to give him a ...