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 Erdos asserted that
every graph is common. Thomason disproved both conjectures by showing that the
complete graph of order four is not common. It is now known that in fact the
common graphs are very rare. Answering a question of Sidorenko and of Jagger,
Stovicek 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.Comment: 9 page
