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 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Grotzsch's theorem (Wikipedia)
Sources
1. Grotzsch's theorem (Wikipedia)
2. Grotzsch's theorem (Wikipedia)
The theorem is named after German mathematician Herbert Grotzsch, who published its proof in 1959View the Source Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.