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.

Let G be a graph and k a natural number. A k-coloring of G is a map c that maps the vertices of G into the set {1, 2, ..., k} (whose elements are called colors) such that no two 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 ...

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 ...

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 ...

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 ...

Here’s a scary scenario: You’ve been put in charge of air traffic control at Newark airport near New York. You need to make sure every plane can taxi between the runway and its gate without hitting ...

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, ...

Researchers have created a new computing system that aims to tackle one of computing's hardest problems in a fraction of the time. Some problems are so challenging to solve that even the most advanced ...