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 ...

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 ...

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 ...

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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 ...

This is a preview. Log in through your library . Abstract This paper describes the application of a vertex coloring procedure to a real life examination scheduling problem. The accessories used in ...

Conjecture 1: For every surface S there is an integer w such that every graph G embedded in S has a set U of vertices such that |U| w and G - U is 5-choosable. Conjecture 2: For every surface S there ...