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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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