Minimal arc-presentations of some nonalternating knots (Q1384204)

The authors construct arc-presentations of special links and prove the minimality of the arc indices of these. The diagrams of the links considered are sums of strongly alternating tangle diagrams, but not alternating themselves. The construction is only applicable, if a certain graph derived from the diagram contains a certain Hamiltonian path -- for which a general condition cannot be given. Minimality is proved by an unequality connecting the arc index with the Kauffman polynomial of the link, a new result due to H. R. Morton and the first author.