In graph-theoretic terminology, the four-color theorem states that the vertices of every planar graph can be colored with at most four colors so that no two adjacent vertices receive the …

The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not share the …

This page gives a brief summary of a new proof of the Four Color Theorem and a four-coloring algorithm found by Neil Robertson, Daniel P. Sanders, Paul Seymour and Robin Thomas.

The four color theorem states that any map--a division of the plane into any number of regions--can be colored using no more than four colors in such a way that no two adjacent regions …

The Four Color Theorem asserts that any map can have its faces colored with at most four different colors such that no two faces that share an edge are the same color.

The four-color theorem is a mathematical proposition that holds that any two-dimensional map can be shaded using only four colors in such a way that no two adjoining sections will have the …

Jul 23, 2025 · The Four Color Theorem and Kuratowski's Theorem are fundamental concepts in graph theory, a branch of discrete mathematics. The Four Color Theorem states that any …

Feb 1, 2011 · Arthur Cayley showed that if four colours had already been used to colour a map, and a new region was added, it was not always possible to keep the original colouring. Above, …

Erasing an edge of a digon or triangle yields a smaller map, which is four-colorable by induction. This coloring uses at most three colors for the ring, leaving us a free color for the kernel face, …

The Four Color Theorem asserts that every planar graph - and therefore every "map" on the plane or sphere - no matter how large or complex, is 4-colorable. Despite the seeming simplicity of …