Every Planar Map Is Four Colorable. Part I¶
Appel, K., & Haken, W. (1977). Every Planar Map Is Four Colorable. Part I: Discharging. Illinois Journal of Mathematics, 21(3), 429-490.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Graph Coloring
- In mathematics it is the four-color theorem, chromatic-polynomial counting, and bounds via maximum clique and degree.
This sourceProves the four-color theorem; the map/cartography coloring problem that names the pattern, with the planarity bound that also governs political districting.
- In mathematics it is the four-color theorem, chromatic-polynomial counting, and bounds via maximum clique and degree.
Domain-specific¶
- Planarity
- The four-color theorem asserts that every planar graph is 4-colorable
This sourcePart I (discharging) of Appel and Haken's proof of the Four Color Theorem, that every planar map can be coloured with four colours.
SupportedVerified against the source
- The four-color theorem asserts that every planar graph is 4-colorable
Mechanisms¶
- Case-Split Elimination Table
- Its strength is that it makes finite, branching impossibilities tractable and their closure explicit — a disciplined proof by exhaustion
This sourceAppel and Haken use discharging to reduce the four-color problem to an explicit finite unavoidable set of configurations for exhaustive checking.
- Its strength is that it makes finite, branching impossibilities tractable and their closure explicit — a disciplined proof by exhaustion
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