  A metric space (X,d) is monotone if there is a linear order < on X and a
constant c>0 such that d(x,y) < c d(x,z) for all x<y<z in X. Properties of
continuous functions with monotone graph (considered as a planar set) are
investigated. It is shown, e.g., that such a function can be almost nowhere
differentiable, but must be differentiable at a dense set, and that Hausdorff
dimension of the graph of such a function is 1.
