Vertex-distinguishing edge-colorings of 2-regular graphs
โ Scribed by P. Wittmann
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 755 KB
- Volume
- 79
- Category
- Article
- ISSN
- 0166-218X
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โฆ Synopsis
Aigner et al., proved that for the irregular coloring number c(G) of a simple 2-regular graph of order n the inequality c(G) < v'& + 0( 1) holds. Here it is shown that c(G) < & + 0( 1).
๐ SIMILAR VOLUMES
We prove the conjecture of Burris and Schelp: a coloring of the edges of a graph of order n such that a vertex is not incident with two edges of the same color and any two vertices are incident with different sets of colors is possible using at most n+1 colors. 1999 Academic Press ## 1. Introducti
An edge-coloring is called vertex-distinguishing if every two distinct vertices are incident to different sets of colored edges. The minimum number of colors required for a vertex-distinguishing proper edge-coloring of a simple graph G is denoted by ฯ s (G). A simple count shows that ฯ s (G) โฅ max{(
## Abstract We associate partitions of the edgeโset of a 4โregular plane graph into 1โfactors or 2โfactors to certain 3โvalued vertex signatures in the spirit of the work by H. Grรถtzsch [1]. As a corollary we obtain a simple proof of a result of F. Jaeger and H. Shank [2] on the edgeโ4โcolorability