## Abstract A. Vince introduced a natural generalization of graph coloring and proved some basic facts, revealing it to be a concept of interest. His work relies on continuous methods. In this note we make some simple observations that lead to a purely combinatorial treatment. Our methods yield sho
Note on the Number of Distinct Chromaticities
β Scribed by MACADAM, D. L.
- Book ID
- 115376838
- Publisher
- Optical Society of America
- Year
- 1947
- Weight
- 624 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0030-3941
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Let Ξ»(__G__) be the lineβdistinguishing chromatic number and __x__β²(__G__) the chromatic index of a graph __G__. We prove the relation Ξ»(__G__) β₯ __x__β²(__G__), conjectured by Harary and Plantholt. Β© 1993 John Wiley & Sons, Inc.
It is shown that the n t h chromatic numbers of the Grotzsch graph provide the answer to an issue raised by
The \(m\)-bounded chromatic number of a graph \(G\) is the smallest number of colors required for a proper coloring of \(G\) in which each color is used at most \(m\) times. We will establish an exact formula for the \(m\)-bounded chromatic number of a tree.