## Abstract Given an edge coloring __F__ of a graph __G__, a vertex coloring of __G__ is __adapted to F__ if no color appears at the same time on an edge and on its two endpoints. If for some integer __k__, a graph __G__ is such that given any list assignment __L__ to the vertices of __G__, with |_
Acyclic list 7-coloring of planar graphs
✍ Scribed by O. V. Borodin; D. G. Fon-Der Flaass; A. V. Kostochka; A. Raspaud; E. Sopena
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 83 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
The acyclic list chromatic number of every planar graph is proved to be at most 7. © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 83–90, 2002
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An __acyclic__ edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The __acyclic chromatic index__ of a graph is the minimum number __k__ such that there is an acyclic edge coloring using __k__ colors and is denoted by __a__′(__G__). It was conjectured by Al
## Abstract A __star coloring__ of a graph is a proper vertex‐coloring such that no path on four vertices is 2‐colored. We prove that the vertices of every planar graph of girth 6 (respectively 7, 8) can be star colored from lists of size 8 (respectively 7, 6). We give an example of a planar graph
## Abstract An __acyclic__ edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The __acyclic chromatic index__ of a graph is the minimum number __k__ such that there is an acyclic edge coloring using __k__ colors and is denoted by __a__′(__G__). A graph is
An __acyclic edge‐coloring__ of a graph is a proper edge‐coloring such that the subgraph induced by the edges of any two colors is acyclic. The __acyclic chromatic index__ of a graph __G__ is the smallest number of colors in an acyclic edge‐coloring of __G__. We prove that the acyclic chromatic inde
## Abstract A proper coloring of the edges of a graph __G__ is called __acyclic__ if there is no 2‐colored cycle in __G__. The __acyclic edge chromatic number__ of __G__, denoted by __a′__(__G__), is the least number of colors in an acyclic edge coloring of __G__. For certain graphs __G__, __a′__(_