## 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
Easier proofs of coloring theorems
✍ Scribed by Jan van Mill
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 90 KB
- Volume
- 97
- Category
- Article
- ISSN
- 0166-8641
No coin nor oath required. For personal study only.
✦ Synopsis
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.
📜 SIMILAR VOLUMES
## Abstract We give proofs of Ore's theorem on Hamilton circuits, Brooks' theorem on vertex coloring, and Vizing's theorem on edge coloring, as well as the Chvátal‐Lovász theorem on semi‐kernels, a theorem of Lu on spanning arborescences of tournaments, and a theorem of Gutin on diameters of orient
An extension of the Kruskal-Katona theorem to colored hypergraphs was given by Frankl, Fiiredi and Kalai in [Shadows of colored complexes, Mathematics Scandinavica]. Here we give a new simple proof.
## Abstract Boolos's proof of incompleteness is extended straightforwardly to yield simple “diagonalization‐free” proofs of some classical limitative theorems of logic. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)