We investigate the relation between the multichromatic number (discussed by Stahl and by Hilton, Rado and Scott) and the star chromatic number (introduced by Vince) of a graph. Denoting these by ฯ \* and ฮท \* , the work of the above authors shows that ฯ \* (G) = ฮท \* (G) if G is bipartite, an odd cy
Star chromatic number
โ Scribed by A. Vince
- Publisher
- John Wiley and Sons
- Year
- 1988
- Tongue
- English
- Weight
- 393 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0364-9024
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๐ SIMILAR VOLUMES
The star-chromatic number of a graph, a parameter introduced by Vince, is a natural generalization of the chromatic number of a graph. Here we construct planar graphs with star-chromatic number r, where r is any rational number between 2 and 3, partially answering a question of Vince.
## Abstract We study a generalization of the notion of the chromatic number of a graph in which the colors assigned to adjacent vertices are required to be, in a certain sense, far apart. ยฉ 1993 John Wiley & Sons, Inc.
## Abstract A. Vince introduced a natural generalization of graph coloring and proved some basic facts, revealing it to be a concept of interest. His work relies on continuous methods. In this note we make some simple observations that lead to a purely combinatorial treatment. Our methods yield sho
The concept of the star chromatic number of a graph was introduced by Vince (A. Vince, Star chromatic number, J. Graph Theory 12 (1988), 551--559), which is a natural generalization of the chromatic number of a graph. This paper calculates the star chromatic numbers of three infinite families of pla
## Abstract We investigate the asymptotics of the size Ramsey number __รฎ__(__K__~1,__n__~__F__), where __K__~1,__n__~ is the __n__โstar and __F__ is a fixed graph. The author 11 has recently proved that __rฬ__(__K__~1,n~,__F__)=(1+__o__(1))__n__^2^ for any __F__ with chromatic number ฯ(__F__)=3. He