This allows for the definition of the anti-van derWaerden number of a graph, which is the least positive integer r such that every exact r-coloring of a graph contains a rainbow k-term arithmetic ...

Graph colouring remains a central topic in graph theory, providing the mathematical framework for assigning colours to the elements of a graph under specific constraints. In particular, the ...

When coloring a graph, every node in a mutually connected cluster, or “clique,” must receive a distinct color, so any graph needs at least as many colors as the number of nodes in its largest clique.

Graph coloring has been employed since the 1980s to efficiently compute sparse Jacobian and Hessian matrices using either finite differences or automatic differentiation. Several coloring problems ...

This paper describes the application of a vertex coloring procedure to a real life examination scheduling problem. The accessories used in deriving and compressing the schedule and in rearranging the ...