Abstract
The on-line list colouring of binomial random graphs \(\mathcal{G}(n,p)\) is studied. We show that the on-line choice number of \(\mathcal{G}(n,p)\) is asymptotically almost surely asymptotic to the chromatic number of \(\mathcal{G}(n,p)\), provided that the average degree d = p(n − 1) tends to infinity faster than (loglogn)1∕3(logn)2 n 2∕3. For sparser graphs, we are slightly less successful; we show that if d ≥ (logn)2+ɛ for some ɛ > 0, then the on-line choice number is larger than the chromatic number by at most a multiplicative factor of C, where C ∈ [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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Acknowledgements
The first author is supported in part by NSF Grant CCF0502793. The fourth author is supported in part by NSERC.
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Frieze, A., Mitsche, D., Pérez-Giménez, X., Prałat, P. (2017). On-Line List Colouring of Random Graphs. In: Díaz, J., Kirousis, L., Ortiz-Gracia, L., Serna, M. (eds) Extended Abstracts Summer 2015. Trends in Mathematics(), vol 6. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-51753-7_8
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DOI: https://doi.org/10.1007/978-3-319-51753-7_8
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