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arXiv · 1501.07469

On-line list colouring of random graphs

Alan Frieze·Dieter Mitsche·Xavier Pérez-Giménez·Paweł Prałat
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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.

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Alan Frieze, Dieter Mitsche, Xavier Pérez-Giménez, Paweł Prałat. 2015-05-12. On-line list colouring of random graphs. https://arxiv.org/abs/1501.07469

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