Given a finite set T of positive integers containing {0}, a T-coloring of a simple graph G is a nonnegative integer function f defined on the vertex set of G, such that if (u, v} E E(G) then Lf(u) -f (u)l $ T. The T-span of a T-coloring is defined as the difference of the largest and smallest colors
Iterated colorings of graphs
โ Scribed by Sandra M Hedetniemi; Stephen T Hedetniemi; Alice A McRae; Dee Parks; Jan Arne Telle
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 786 KB
- Volume
- 278
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
A 2-assignment on a graph G (V,E) is a collection of pairs Lv of allowed colors speciยฎed for all vertices v PV. The graph G (with at least one edge) is said to have oriented choice number 2 if it admits an orientation which satisยฎes the following property: For every 2-assignment there exists a choic
In this article, we introduce the new notion of acyclic improper colorings of graphs. An improper coloring of a graph is a vertex-coloring in which adjacent vertices are allowed to have the same color, but each color class V i satisfies some condition depending on i. Such a coloring is acyclic if th
## Abstract A proper coloring of the edges of a graph __G__ is called __acyclic__ if there is no 2โcolored cycle in __G__. The __acyclic edge chromatic number__ of __G__, denoted by __aโฒ__(__G__), is the least number of colors in an acyclic edge coloring of __G__. For certain graphs __G__, __aโฒ__(_