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.
The star chromatic number of a graph
β Scribed by H. L. Abbott; B. Zhou
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 469 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
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. Β© 1993 John Wiley & Sons, Inc.
π SIMILAR VOLUMES
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
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 Ο \* and Ξ· \* , the work of the above authors shows that Ο \* (G) = Ξ· \* (G) if G is bipartite, an odd cy
Following [1] , we investigate the problem of covering a graph G with induced subgraphs G 1 ; . . . ; G k of possibly smaller chromatic number, but such that for every vertex u of G, the sum of reciprocals of the chromatic numbers of the G i 's containing u is at least 1. The existence of such ''ch
## Abstract Star chromatic number, introduced by A. Vince, is a natural generalization of chromatic number. We consider the question, βWhen is Ο\* < Ο?β We show that Ο\* < Ο if and only if a particular digraph is acyclic and that the decisioin problem associated with this question is probably not i