## Abstract The ErdΕsβSΓ³s Conjecture is that a finite graph __G__ with average degree greater than __k__βββ2 contains every tree with __k__ vertices. Theorem 1 is a special case: every __k__βvertex tree of diameter four can be embedded in __G__. A more technical result, Theorem 2, is obtained by ex
Some probabilistic restatements of the Four Color Conjecture
β Scribed by Yuri Matiyasevich
- Publisher
- John Wiley and Sons
- Year
- 2004
- Tongue
- English
- Weight
- 99 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
With every triangulation of sphere, we associate a probabilistic space in a natural way and define several random events. The Four Color Conjecture (4CC) turns out to be equivalent to different statements about positive correlation among some pairs of these events. Β© 2004 Wiley Periodicals, Inc. J Graph Theory 46: 167β179, 2004
π SIMILAR VOLUMES
We prove more special cases of the Fontaine Mazur conjecture regarding p-adic Galois representations unramified at p, and we present evidence for and consequences of a generalization of it. ## 1999 Academic Press Conjecture 1 (Fontaine, Mazur). There do not exist a number field K and an infinite e
## 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 twoβpart article outlines the nature and