We show that if the adjacency matrix of a graph X has 2-rank 2r, then the chromatic number of X is at most 2 r +1, and that this bound is tight. 2001
The gap between the chromatic number of a graph and the rank of its adjacency matrix is superlinear
β Scribed by A.A. Razborov
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 199 KB
- Volume
- 108
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
The gap between the chromatic number of a graph and the rank of its adjacency matrix is superlinear.
π SIMILAR VOLUMES
Upper bounds for u + x and ax are proved, where u is the domination number and x the chromatic number of a graph.
## 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.
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 Let Ξ»(__G__) be the lineβdistinguishing chromatic number and __x__β²(__G__) the chromatic index of a graph __G__. We prove the relation Ξ»(__G__) β₯ __x__β²(__G__), conjectured by Harary and Plantholt. Β© 1993 John Wiley & Sons, Inc.
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