This research topic explores the theoretical foundations and practical applications of graph labeling and coloring problems, both of which are central to modern combinatorics and computer science.

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 ...

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 ...

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 ...

Consider an urn model where at each step one of q colors is sampled according to some probability distribution and a ball of that color is placed in an urn. The distribution of assigning balls to urns ...

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 ...

The so-called differential equation method in probabilistic combinatorics presented by Patrick Bennett, Ph.D., Department of Mathematics, Western Michigan University Abstract: Differential equations ...