The De Bruijn-Erdos theorem, in graph theory, states that if every finite subgraph of an infinite graph can be properly colored with c colors, then the whole graph can also be colored with c colors. Proved by Nicolaas Govert de Bruijn and Paul Erdos, the theorem depends essentially on the axiom of choice in every known proof, and it is used to extend results such as the four color theorem and Dilworth's theorem from finite to infinite graphs, and to reduce the Hadwiger-Nelson problem to a question about finite graphs. 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 FormCharacterization Theorem 1 Connections
Has Statement Form
In Branch
Source De Bruijn-Erdos theorem (graph theory) (Wikipedia)
Proved By
Source De Bruijn-Erdos theorem (graph theory) (Wikipedia)
Source De Bruijn-Erdos theorem (graph theory) (Wikipedia)
Sources
1. De Bruijn-Erdos theorem (graph theory) (Wikipedia)
Lead section
In graph theory, the De Bruijn-Erdős theorem relates graph coloring of an infinite graph to the same problem on its finite subgraphs.
In Group: Graph Theory, Lead
In graph theory, the De Bruijn-Erdős theorem relates graph coloring of an infinite graph to the same problem on its finite subgraphs.
In Branch: Graph Theory, Lead
In graph theory, the De Bruijn-Erdős theorem relates graph coloring of an infinite graph to the same problem on its finite subgraphs.
Proved By: Nicolaas Govert de Bruijn, Lead
The theorem was proved by Nicolaas Govert de Bruijn and Paul Erdős, after whom it is named.
Proved By: Paul Erdos, Lead
The theorem was proved by Nicolaas Govert de Bruijn and Paul Erdős, after whom it is named.
View the SourceReader 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.