## Abstract Given a simple plane graph __G__, an edge‐face __k__‐coloring of __G__ is a function ϕ : __E__(__G__) ∪ __F__(G) → {1,…,__k__} such that, for any two adjacent or incident elements __a__, __b__ ∈ __E__(__G__) ∪ __F__(__G__), ϕ(__a__) ≠ ϕ(__b__). Let χ~e~(__G__), χ~ef~(__G__), and Δ(__G_
On the d-distance face chromatic number of plane graphs
✍ Scribed by Mirko Horňák; Stanislav Jendrol'
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 223 KB
- Volume
- 164
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
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 connected plane graphs with maximum degree at least eight.
📜 SIMILAR VOLUMES
## A b&act Voigt, M. and H. Walther, On the chromatic number of special distance graphs, Discrete Mathematics 97 (1991) 395-397. For all 12 10 and u 2 1' -61+ 3 the chromatic number is proved to be 3 for distance graphs with all integers as vertices, and edges only if the vertices are at distance
Let G be a planar graph. The vertex face total chromatic number ,y13(G) of G is the least number of colors assigned to V(G) U F(G) such that no adjacent or incident elements receive the same color. The main results of this paper are as follows: (1) We give the vertex face total chromatic number for
In this paper, we shall first prove that for a Halin graph G, 4 °xT (G) °6, where x T (G) is the vertex-face total chromatic number of G. Second, we shall establish a sufficient condition for a Halin graph to have a vertex-face total chromatic number of 6. Finally, we shall give a necessary and suff