The interval number of a graph G, denoted by i(G), is the least natural number t such that G is the intersection graph of sets, each of which is the union of at most t intervals. Here we settle a conjecture of Griggs and West about bounding i(G) in terms of e, that is, the number of edges in G. Name
Sharp bounds on the order, size, and stability number of graphs
β Scribed by Pierre Hansen; Maolin Zheng
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 276 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
We consider graphs G = (V,E) with order Ο = |V|, size e = |E|, and stability number Ξ²~0~. We collect or determine upper and lower bounds on each of these parameters expressed as functions of the two others. We prove that all these bounds are sharp. Β© 1993 by John Wiley & Sons, Inc.
π SIMILAR VOLUMES
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## Abstract A new lower bound on the number of nonβisomorphic Hadamard symmetric designs of even order is proved. The new bound improves the bound on the number of Hadamard designs of order 2__n__ given in [12] by a factor of 8__n__βββ1 for every odd __n__β>β1, and for every even __n__ such that 4_
## Abstract In this article we first give an upper bound for the chromatic number of a graph in terms of its degrees. This bound generalizes and modifies the bound given in 11. Next, we obtain an upper bound of the order of magnitude ${\cal O}({n}^{{1}-\epsilon})$ for the coloring number of a graph