Asteroidal Chromatic Number of a Graph
โ Scribed by S. Arumugam; Hepzibai Jeyakumar
- Book ID
- 108498071
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 185 KB
- Volume
- 15
- Category
- Article
- ISSN
- 1571-0653
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
It was proved (A. Kotlov and L. Lovรกsz, The rank and size of graphs, J. Graph Theory 23 (1996), 185-189) that the number of vertices in a twin-free graph is O(( โ 2) r ) where r is the rank of the adjacency matrix. This bound was shown to be tight. We show that the chromatic number of a graph is o(โ
## 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
The harmonious chromatic number of a graph G, denoted by h(G), is the least number of colon which can be assigned to the vertices of G such that adjacent vertices are colored differently and any two distinct edges have different color pairs. This is a slight variation of a definition given independe