On-line list colouring of random graphs
Combinatorics
2015-05-13 v2 Discrete Mathematics
Abstract
In this paper, the on-line list colouring of binomial random graphs G(n,p) is studied. We show that the on-line choice number of G(n,p) is asymptotically almost surely asymptotic to the chromatic number of G(n,p), provided that the average degree d=p(n-1) tends to infinity faster than (log log n)^1/3(log n)^2n^(2/3). For sparser graphs, we are slightly less successful; we show that if d>(log n)^(2+epsilon) for some epsilon>0, then the on-line choice number is larger than the chromatic number by at most a multiplicative factor of C, where C in [2,4], depending on the range of d. Also, for d=O(1), the on-line choice number is by at most a multiplicative constant factor larger than the chromatic number.
Keywords
Cite
@article{arxiv.1501.07469,
title = {On-line list colouring of random graphs},
author = {Alan Frieze and Dieter Mitsche and Xavier Pérez-Giménez and Paweł Prałat},
journal= {arXiv preprint arXiv:1501.07469},
year = {2015}
}