A note on the star chromatic number
β Scribed by J. A. Bondy; Pavol Hell
- Publisher
- John Wiley and Sons
- Year
- 1990
- Tongue
- English
- Weight
- 176 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
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 shorter proofs and offer further insight.
π SIMILAR VOLUMES
## Abstract We study a generalization of the notion of the chromatic number of a graph in which the colors assigned to adjacent vertices are required to be, in a certain sense, far apart. Β© 1993 John Wiley & Sons, Inc.
## 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.
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.
The star-chromatic number of a graph, a parameter introduced by Vince, is a natural generalization of the chromatic number of a graph. Here we construct planar graphs with star-chromatic number r, where r is any rational number between 2 and 3, partially answering a question of Vince.
We investigate the notion of the star chromatic number of a graph in conjunction with various other graph parameters, among them, clique number, girth, and independence number. 1997 Academic Press /\*(G)=inf { m d : G has an (m, d )&coloring = . article no. TB961738 245 0095-8956Γ97 25.00