## 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
A note on the line-distinguishing chromatic number and the chromatic index of a graph
β Scribed by N. Zagaglia Salvi
- Publisher
- John Wiley and Sons
- Year
- 1993
- Tongue
- English
- Weight
- 126 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
Let Ξ»(G) be the lineβdistinguishing chromatic number and xβ²(G) the chromatic index of a graph G.
We prove the relation Ξ»(G) β₯ xβ²(G), conjectured by Harary and Plantholt. Β© 1993 John Wiley & Sons, Inc.
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.
Following [1] , we investigate the problem of covering a graph G with induced subgraphs G 1 ; . . . ; G k of possibly smaller chromatic number, but such that for every vertex u of G, the sum of reciprocals of the chromatic numbers of the G i 's containing u is at least 1. The existence of such ''ch
We show that if the adjacency matrix of a graph X has 2-rank 2r, then the chromatic number of X is at most 2 r +1, and that this bound is tight. 2001
## Abstract It was only recently shown by Shi and Wormald, using the differential equation method to analyze an appropriate algorithm, that a random 5βregular graph asymptotically almost surely has chromatic number at most 4. Here, we show that the chromatic number of a random 5βregular graph is as