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
Bounds for the covering number of a graph
β Scribed by H.L. Abbott; A.C. Liu
- Publisher
- Elsevier Science
- Year
- 1979
- Tongue
- English
- Weight
- 333 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract The upper bound for the harmonious chromatic number of a graph given by Zhikang Lu and by C. McDiarmid and Luo Xinhua, independently (__Journal of Graph Theory__, 1991, pp. 345β347 and 629β636) and the lower bound given by D. G. Beane, N. L. Biggs, and B. J. Wilson (__Journal of Graph T
## Abstract After giving a new proof of a wellβknown theorem of Dirac on critical graphs, we discuss the elegant upper bounds of Matula and SzekeresβWilf which follow from it. In order to improve these bounds, we consider the following fundamental coloring problem: given an edgeβcut (__V__~1~, __V_
## Abstract Bounds are determined for the Ramsey number of the union of graphs versus a fixed graph __H__, based on the Ramsey number of the components versus __H__. For certain unions of graphs, the exact Ramsey number is determined. From these formulas, some new Ramsey numbers are indicated. In p
The bondage number b(G) of a graph G is the minimum cardinality of a set of edges of G whose removal from G results in a graph with domination number larger than that of G. Several new sharp upper bounds for b(G) are established. In addition, we present an infinite class of graphs each of whose bond