On the Number of Plane Geometric Graphs
β Scribed by Oswin Aichholzer; Thomas Hackl; Clemens Huemer; Ferran Hurtado; Hannes Krasser; Birgit Vogtenhuber
- Publisher
- Springer Japan
- Year
- 2007
- Tongue
- English
- Weight
- 262 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The d-distance face chromatic number of a connected plane graph G is the minimum number of colours in such a colouring of faces of G that whenever two distinct faces are at the distance at most d, they receive distinct colours. We estimate the d-distance face chromatic number from above for connecte
In 1973, Kronk and Mitchem (Discrete Math. (5) 255-260) conjectured that the vertices, edges and faces of each plane graph G may be colored with D(G) + 4 colors, where D(G) is the maximum degree of G, so that any two adjacent or incident elements receive distinct colors. They succeeded in verifying
The entire chromatic number Ο ve f (G) of a plane graph G is the least number of colors assigned to the vertices, edges and faces so that every two adjacent or incident pair of them receive different colors. conjectured that Ο ve f (G) β€ + 4 for every plane graph G. In this paper we prove the conj
## 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_