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A new upper bound for the list chromatic number. (English) Zbl 0674.05027
In this paper it is proved, using some arguments from the theory of random graphs, that if \(\Delta\) is sufficiently large, then for every graph G with maximum degree \(\Delta (G)=\Delta\), we have \(\chi '_{\ell}(G)\leq 7\Delta /4+\lceil 25\) log \(\Delta\) \(\rceil.\)
The authors assert that it is possible to give a slightly improved value for the above upper bound for the list chromatic number, namely \(\chi '_{\ell}(G)\leq 12\Delta /7+o(\Delta)\), but this improvement has a proof which is more lengthy and does not add significantly to the proof techniques for boundary \(\chi '_{\ell}\).
Reviewer: I.Tomescu

MSC:
05C15 Coloring of graphs and hypergraphs
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References:
[1] Bollobás, B., Random graphs, (1985), Academic Press London · Zbl 0567.05042
[2] Bollobás, B.; Harris, A.J., List-colourings of graphs, Graphs and combinatorics, 1, 115-127, (1985) · Zbl 0606.05027
[3] A. Chetwynd and R. Häggkvist, A note on list-colourings, manuscript.
[4] Erdös, P.; Rubin, A.; Taylor, H., Choosability in graphs, Congressus numerantum, 26, 125-157, (1979)
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