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Lower bounds for chromatic number of a graph
In this article, table 4, optimization-online.org/DB_HTML/2010/03/2568.html there are results for a time bound of 3600 seconds. Whether the fractional chromatic number problem for a graph of 560 vertices can be solved within this time bound depends on the type of graph. From the table it seems that denser graphs are more likely to be solved earlier.
|Lower bounds for chromatic number of a graph|