+\rem
+The bound on the average degree needed to enforce a~$K_k$ minor, which we get from Theorem \ref{maderthm},
+is very coarse. Kostochka \cite{kostochka:lbh} and independently Thomason \cite{thomason:efc}
+have proven that an~average degree $\Omega(k\sqrt{\log k})$ is sufficient and that this
+is the best what we can get.
+
+\rem
+Minor-closed classes share many other interesting properties, for example bounded chromatic
+numbers of various kinds, as shown by Theorem 6.1 of \cite{nesetril:minors}. We can expect
+that many algorithmic problems will turn out to be easy for them.
+