A partial ordering of knots and links through diagrammatic unknotting

In this paper we de. ne a partial ordering of knots and links using a special property derived from their minimal diagrams. A link K' is called a predecessor of a link K if Cr(K') < Cr(K) and a diagram of K' can be obtained from a minimal diagram D of K by a single crossing change. In such a case, we say that K' < K. We investigate the sets of links that can be obtained by single crossing changes over all minimal diagrams of a given link. We show that these sets are specific for different links and permit partial ordering of all links. Some interesting results are presented and many questions are raised.