still only a partial solution

Once again, the paper cited offers only a partial solution. Quoting from the paper, "From Theorem 1.1, we conclude that the strong chromatic number can be bounded by $ 2\Delta(G) $ if $ |V(G)| \le 6\Delta(G) $. This result should not be compared with the more complete and difficult result of Alon." Here, the difficult result of Alon is the theorem that there exists a fixed constant $ K $ so that every graph of maximum degree $ \Delta $ is strongly $ K \Delta $-colorable.. precisely the result which is sharpened by this conjecture.


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