## Abstract Given a simple plane graph __G__, an edgeβface __k__βcoloring of __G__ is a function Ο : __E__(__G__) βͺ __F__(G)βββ {1,β¦,__k__} such that, for any two adjacent or incident elements __a__, __b__ β __E__(__G__) βͺ __F__(__G__), Ο(__a__)ββ βΟ(__b__). Let Ο~e~(__G__), Ο~ef~(__G__), and Ξ(__G_
Axiom of choice and chromatic number of the plane
β Scribed by Saharon Shelah; Alexander Soifer
- Book ID
- 108396269
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 110 KB
- Volume
- 103
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Comprehensive in its selection of topics and results, this self-contained text examines the relative strengths and the consequences of the axiom of choice. Subjects include consistency and independence, permutation models, and examples and counterexamples of the axiom's use. Each chapter contains se
## Abstract For a finite projective plane $\Pi$, let $\bar {\chi} (\Pi)$ denote the maximum number of classes in a partition of the point set, such that each line has at least two points in the same partition class. We prove that the best possible general estimate in terms of the order of projectiv