Definitions of criticality with respect to edge-coloring
β Scribed by A. J. W. Helton
- Publisher
- John Wiley and Sons
- Year
- 1977
- Tongue
- English
- Weight
- 310 KB
- Volume
- 1
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
Here we examine six definitions of criticality concerning the chromatic index (edge chromatic number) of a simple graph. Five of these turn out to be almost always almost equivalent. Some problems arise and some conjectures are posed.
π SIMILAR VOLUMES
A colouring of the vertices of a hypergraph G is called strong if, for every edge A, the colours of all vertices in A are distinct. It corresponds to a colouring of the generated graph (G) obtained from G by replacing every edge by a clique. We estimate the minimum number of edges possible in a k-cr
It is shown. that for every infinite cardinal \(\kappa\) there exists a graph \(F\) on \(\kappa\) vertices satisfying \(F \rightarrow(T)_{i}^{\text {edgen }}\) for every tree \(T\) on \(\kappa\) vertices and all \(i\) satisfying cf \(\kappa \rightarrow((1))_{j}^{3}\). ' 1993 Acadenic Press, Inc.
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