On parsimonious edge-colouring of graphs with maximum degree three

Details On parsimonious edge-colouring of graphs with maximum degree three On parsimonious edge-colouring of graphs with maximum degree three

2008-09-27

arxiv.org/abs/0809.4747v6

Computer Science

Discrete Mathematics

Revised version submitted to Graphs and Combinatorics

Scientific paper

In a graph $G$ of maximum degree $\Delta$ let $\gamma$ denote the largest fraction of edges that can be $\Delta$ edge-coloured. Albertson and Haas showed that $\gamma \geq 13/15$ when $G$ is cubic . We show here that this result can be extended to graphs with maximum degree 3 with the exception of a graph on 5 vertices. Moreover, there are exactly two graphs with maximum degree 3 (one being obviously the Petersen graph) for which $\gamma = 13/15$. This extends a result given by Steffen. These results are obtained by using structural properties of the so called $\delta$-minimum edge colourings for graphs with maximum degree 3. Keywords : Cubic graph; Edge-colouring

Affiliated with

Also associated with

No associations

Rating

On parsimonious edge-colouring of graphs with maximum degree three does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On parsimonious edge-colouring of graphs with maximum degree three, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On parsimonious edge-colouring of graphs with maximum degree three will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-653600