  We say that a link $L_1$ is an s-major of a link $L_2$ if any diagram of
$L_1$ can be transformed into a diagram of $L_2$ by changing some crossings and
smoothing some crossings. This relation is a partial ordering on the set of all
prime alternating links. We determine this partial order for all prime
alternating knots and links with the crossing number less than or equal to six.
The proofs are given by graph-theoretic methods.
