A Colorful Proof of Pick’s Theorem
✍ Scribed by International Monetary Fund,
- Book ID
- 115447477
- Publisher
- Informa UK (Taylor & Francis)
- Year
- 2010
- Weight
- 574 KB
- Volume
- 18
- Category
- Article
- ISSN
- 1072-4117
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📜 SIMILAR VOLUMES
We present a simpler proof of the known theorem that a fixed-point free homeomorphism on an n-dimensional paracompact space can be colored with n + 3 colors.
A simple proof of Grfinbaum's theorem on the 3-colourability of planar graphs having at most three 3-cycles is given, which does not employ the colouring extension. In 1958, Gr6tzsch I-5] proved that every planar graph without cycles of length three is 3-colourable. In 1963, Griinbaum [6] extended
## Abstract In 1965 Ringel raised a 6 color problem for graphs that can be stated in at least three different forms. In particular, is it possible to color the vertices and faces of every plane graph with 6 colors so that any two adjacent or incident elements are colored differently? This 6 color p