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 ...

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 ...

In 1852, botanist Francis Guthrie noticed something peculiar as he was coloring a map of counties in England. Despite the counties’ meandering shapes and varied configurations, four colors were all he ...

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 ...

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 ...

Four years ago, the mathematician Maria Chudnovsky faced an all-too-common predicament: how to seat 120 wedding guests, some of whom did not get along, at a dozen or so conflict-free tables. Luckily, ...

Fifty years ago, Paul Erdős and two other mathematicians came up with a graph theory problem that they thought they might solve on the spot. A team of mathematicians has finally settled it. In the ...

If true, the following conjecture of Thomassen [Th81] is a planarity criterion for a special class of graphs that involves only K 5. Recall that a planar graph on n vertices contains at most 3n-6 ...

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 ...

Jonathan Hulgan does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond ...