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.

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 ...

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 ...

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 ...

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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 ...