The chromatic number of the complementary graph to a simple graph associated with a commutative ring
โ Scribed by Sato, Junro; Baba, Kiyoshi
- Book ID
- 125386278
- Publisher
- Springer-Verlag
- Year
- 2014
- Tongue
- English
- Weight
- 296 KB
- Volume
- 3
- Category
- Article
- ISSN
- 2193-5343
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## 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.
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
For each commutative ring R we associate a simple graph โซ R . We investigate the interplay between the ring-theoretic properties of R and the graph-theo-ลฝ . retic properties of โซ R .