These notes constitute an exploration in comblnatortol
and knot theory. Knots and links in three-dimensional .,ao.
may be understood through their planar projections. A knot
is usually drawn as a schematic snapshot, with crossings indicated
by broken line segments. ThUS~ represents the
trefoil knot. We shall refer to such a picture &s & ~
diagram. The projection corresponding to .uch & diagram
forms a (directed) multi-graph in the plane, with tour ed,e.
incident to each vertex. We shall study these graphs .eparately,
and for their own sake.