Grötzsch's theorem

In graph theory, a branch of mathematics, the set of Grötzsch is declining on Herbert Grötzsch theorem on the colorability of graphs with three colors.

Dyeability

Staining assigns each node of a graph to a color so that the nodes are each edge colored with different colors. We want to know the minimum number of colors needed for coloring of a given graph. The four-color theorem states that every planar graph can be dyed with four colors. The set of Grötzsch answers the question of which planar graph be colored with three colors even.

Set of Grötzsch

A triangle-free planar graph can be colored with three colors.

( A graph is called triangle- free if it contains no isomorphic to the complete graph subgraphs. )