  For a real c \geq 1 and an integer n, let f(n,c) denote the maximum integer f
so that every graph on n vertices contains an induced subgraph on at least f
vertices in which the maximum degree is at most c times the minimum degree.
Thus, in particular, every graph on n vertices contains a regular induced
subgraph on at least f(n,1) vertices. The problem of estimating $(n,1) was
posed long time ago by Erdos, Fajtlowicz and Staton. In this note we obtain the
following upper and lower bounds for the asymptotic behavior of f(n,c):
  (i) For fixed c>2.1, n^{1-O(1/c)} \leq f(n,c) \leq O(cn/\log n).
  (ii) For fixed c=1+\epsilon with epsilon>0 sufficiently small, f(n,c) \geq
n^{\Omega(\epsilon^2/ \ln (1/\epsilon))}.
  (iii) \Omega (\ln n) \leq f(n,1) \leq O(n^{1/2} \ln^{3/4} n).
  An analogous problem for not necessarily induced subgraphs is briefly
considered as well.
