Acyclic total colorings of planar graphs withoutlcycles
β Scribed by Xiang Yong Sun; Jian Liang Wu
- Publisher
- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2011
- Tongue
- English
- Weight
- 194 KB
- Volume
- 27
- Category
- Article
- ISSN
- 1439-7617
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract The acyclic list chromatic number of every planar graph is proved to be at most 7. Β© 2002 Wiley Periodicals, Inc. J Graph Theory 40: 83β90, 2002
## Abstract A proper coloring of the edges of a graph __G__ is called __acyclic__ if there is no 2βcolored cycle in __G__. The __acyclic edge chromatic number__ of __G__, denoted by __aβ²__(__G__), is the least number of colors in an acyclic edge coloring of __G__. For certain graphs __G__, __aβ²__(_
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__β²(__G__). It was conjectured by Al
It is proved that a planar graph with maximum degree β β₯ 11 has total (vertex-edge) chromatic number β + 1.