Mathematics Atlas

How Proof Is Made
Sign In
Text size
100%
Theme

Switch Atlas

Theorem

Grotzsch's Theorem

Combinatorics and Graph Theory

Grotzsch's theorem, in graph theory, states that every triangle-free planar graph can be properly colored using only three colors. The result sharpens the four color theorem, which guarantees four colors suffice for any planar graph in general, showing that forbidding triangles, meaning sets of three mutually adjacent vertices, lowers the number of colors needed to three. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Classification
Statement Form
Existence Theorem 1
Proof Year
1959 2
Connections

Has Statement Form

Existence Theorem, Concepts

In Branch

Graph Theory, Branches of Mathematics
Source Grotzsch's theorem (Wikipedia)
Sources
1. Grotzsch's theorem (Wikipedia)
  • Lead section
    In the mathematical field of graph theory, Grötzsch's theorem is the statement that every triangle-free planar graph can be colored with only three colors.
  • In Branch: Graph Theory, Lead sentence
View the Source
2. Grotzsch's theorem (Wikipedia)
The theorem is named after German mathematician Herbert Grotzsch, who published its proof in 1959View the Source
Comments (0)
No comments yet. Be the first to share a thought.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.