I made up a set of head scarves for a class I am teaching. I wanted people to be able to experiment with lace, cables, and textures while they learned a few different ways of doing edges and increases.
One is lace, one uses a two-stitche cable (walking stitches) and one has a simple celtic knot cabled into a purled background. They all start at the point and feature knit in ties. The edges have very little roll. I use a couple of different increases throughout both for effect and variety.
They can easily be made for just about any head size. Just stop 1 1/2 to 2 inches short of the head circumference before making the ties. I do suggest a firm yarn, like cotton or linen, with no stretch so that the scarf does not "grow" on you. It has been successfully knit, however, with quite a variety of yarns.