Chromatic numbers of products of graphs: The directed and undirected versions of the Poljak-Rödl function
✍ Scribed by Claude Tardif; David Wehlau
- Publisher
- John Wiley and Sons
- Year
- 2005
- Tongue
- English
- Weight
- 61 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
Let f(n) = min{χ(G × H) : G and H are n‐chromatic digraphs} and g(n) = min{χ(G × H) : G and H are n‐chromatic graphs}. We prove that f is bounded if and only if g is bounded. © 2005 Wiley Periodicals, Inc. J Graph Theory
📜 SIMILAR VOLUMES
Topp, J. and L. Volkmann, Some upper bounds for the product of the domination number and the chromatic number of a graph, Discrete Mathematics 118 (1993) 2899292. Some new upper bounds for yx are proved, where y is the domination number and x is the chromatic number of a graph. All graphs consider
## Abstract Suppose __G__ is a series‐parallel graph. It was proved in 3 that either ~χ__c__~(__G__) = 3 or ~χ__c__~(__G__) ≤ 8/3. So none of the rationals in the interval (8/3, 3) is the circular chromatic number of a series‐parallel graph. This paper proves that for every rational __r__ ∈ [2, 8/3