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Given a map with genus g>0, Heawood showed in 1890 that the maximum number N_u of colors necessary to color a map (the chromatic number) on an unbounded surface is N_u = ...

A coloring of plane regions, link segments, etc., is an assignment of a distinct labeling (which could be a number, letter, color, etc.) to each component. Coloring problems ...

A map is a way of associating unique objects to every element in a given set. So a map f:A|->B from A to B is a function f such that for every a in A, there is a unique ...

Martin Gardner (1975) played an April Fool's joke by asserting that the map of 110 regions illustrated above (left figure) required five colors and constitutes a ...

The number of colors sufficient for map coloring on a surface of genus g is given by the Heawood conjecture, chi(g)=|_1/2(7+sqrt(48g+1))_|, where |_x_| is the floor function. ...

Define a valid "coloring" to occur when no two faces with a common edge share the same color. Given two colors, there is a single way to color an octahedron (Ball and Coxeter ...

A 3-coloring of graph edges so that no two edges of the same color meet at a graph vertex (Ball and Coxeter 1987, pp. 265-266).

A k-coloring of a graph G is a vertex coloring that is an assignment of one of k possible colors to each vertex of G (i.e., a vertex coloring) such that no two adjacent ...

Assignment of each graph edge of a graph to one of two color classes (commonly designation "red" and "green").

A map x|->x^p where p is a prime.