Non-three-colorable Common Graphs Exist
نویسنده
چکیده
A graph H is called common if the total number of copies of H in every graph and its complement asymptotically minimizes for random graphs. A former conjecture of Burr and Rosta, extending a conjecture of Erdős asserted that every graph is common. Thomason disproved both conjectures by showing that K4 is not common. It is now known that in fact the common graphs are very rare. Answering a question of Sidorenko and of Jagger, Šťovíček and Thomason from 1996 we show that the 5-wheel is common. This provides the first example of a common graph that is not three-colorable.
منابع مشابه
Reu 2007
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تاریخ انتشار 2011