S-graphs and braid index of links

Анотація

We study relationship between reduction operations on link diagrams and S-graphs associated with them. We are motivated by the problem of computing the braid index of a link and some well known conjectures concerning the braid index of a link and the writhe of its diagrams. Possible counterexamples are discussed in terms of both S-graphs and link diagrams. We also indicate a relation of S-graphs to singular links regarded up to an appropriate equivalence relation.