On the strong chromatic number of random graphs

Details On the strong chromatic number of random graphs On the strong chromatic number of random graphs

2007-06-14

arxiv.org/abs/0706.2110v1

Mathematics

Combinatorics

16 pages

Scientific paper

Let G be a graph with n vertices, and let k be an integer dividing n. G is said to be strongly k-colorable if for every partition of V(G) into disjoint sets V_1 \cup ... \cup V_r, all of size exactly k, there exists a proper vertex k-coloring of G with each color appearing exactly once in each V_i. In the case when k does not divide n, G is defined to be strongly k-colorable if the graph obtained by adding k \lceil n/k \rceil - n isolated vertices is strongly k-colorable. The strong chromatic number of G is the minimum k for which G is strongly k-colorable. In this paper, we study the behavior of this parameter for the random graph G(n, p). In the dense case when p >> n^{-1/3}, we prove that the strong chromatic number is a.s. concentrated on one value \Delta+1, where \Delta is the maximum degree of the graph. We also obtain several weaker results for sparse random graphs.

Affiliated with

Also associated with

No associations

Rating

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

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-331146