On zero sum Ramsey numbers: Multiple copies of a graph
โ Scribed by A. Bialostocki; P. Dierker
- Publisher
- John Wiley and Sons
- Year
- 1994
- Tongue
- English
- Weight
- 376 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
โฆ Synopsis
Abstract
As a consequence of our main result, a theorem of Schrijver and Seymour that determines the zero sum Ramsey numbers for the family of all rโhypertrees on m edges and a theorem of Bialostocki and Dierker that determines the zero sum Ramsey numbers for rโhypermatchings are combined into a single theorem. Another consequence is the determination of zero sum Ramsey numbers of multiple copies of some small graphs.
๐ SIMILAR VOLUMES
A main result proved in this paper is the following. Theorem. Let G be a noncomplete graph on n vertices with degree sequence where R is the zero-sum Ramsey number.
## Abstract We prove the following generalization of earlier results of Bialostocki and Dierker [3] and Caro [7]. Theorem. Let __t__ โฉพ __k__ โฉพ 2 be positive integers such that __k__ | __t__, and let __c :E__(K) โ โค~__k__~ be a mapping of all the __r__โsubsets of an __rt__ + __k__ โ1 element set in
## Abstract Bounds on the sum and product of the chromatic numbers of __n__ factors of a complete graph of order __p__ are shown to exist. The wellโknown theorem of Nordhaus and Gaddum solves the problem for __n__ = 2. Strict lower and some upper bounds for any __n__ and strict upper bounds for __n