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 ...

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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, ...

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 ...

A theorem for coloring a large class of “perfect” mathematical networks could ease the way for a long-sought general coloring proof. Four years ago, the mathematician Maria Chudnovsky faced an all-too ...

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 collection ...