𝔖 Bobbio Scriptorium
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The four-color theorem for small maps

✍ Scribed by Walter Stromquist


Book ID
107884044
Publisher
Elsevier Science
Year
1975
Tongue
English
Weight
727 KB
Volume
19
Category
Article
ISSN
0095-8956

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πŸ“œ SIMILAR VOLUMES


The combinatorial map color theorem
✍ Gerhard Ringel πŸ“‚ Article πŸ“… 1977 πŸ› John Wiley and Sons 🌐 English βš– 522 KB

## Abstract This paper is written in the spirit of the author's book: __Map Color Theorem__ (1974). We try to develop the Map Color Theorem in a combinatorial way, circumventing the unwieldy embedding theory. Similar (but not identical) generalizations have recently and independently been developed

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It is proved that the choice number of every graph G embedded on a surface of Euler genus Ξ΅ β‰₯ 1 and Ξ΅ = 3 is at most the Heawood number H(Ξ΅) = (7 + √ 24Ξ΅ + 1)/2 and that the equality holds if and only if G contains the complete graph K H(Ξ΅) as a subgraph.

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## Abstract A major event in 1976 was the announcement that the Four Color Conjecture (4CC) had at long last become the Four Color Theorem (4CT). The proof by W. Haken, K. Appel, and J. Koch is published in the __Illinois Journal of Mathematics__, and their two‐part article outlines the nature and