On the chromatic number of random d-regular graphs

Details On the chromatic number of random d-regular graphs On the chromatic number of random d-regular graphs

2008-12-15

arxiv.org/abs/0812.2937v1

Mathematics

Combinatorics

Scientific paper

In this work we show that, for any fixed d, random d-regular graphs asymptotically almost surely can be coloured with k colours, where k is the smallest integer satisfying d<2(k-1)log(k-1). From previous lower bounds due to Molloy and Reed, this establishes the chromatic number to be asymptotically almost surely k-1 or k. If moreover d>(2k-3)log(k-1), then the value k-1 is discarded and thus the chromatic number is exactly determined. Hence we improve a recently announced result by Achlioptas and Moore in which the chromatic number was allowed to take the value k+1. Our proof applies the small subgraph conditioning method to the number of balanced k-colourings, where a colouring is balanced if the number of vertices of each colour is equal.

Affiliated with

Also associated with

No associations

Rating

On the chromatic number of random d-regular graphs 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 the chromatic number of random d-regular graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the chromatic number of random d-regular graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-226388