The braid indices of pretzel links: A comprehensive study, Part I.

In this paper and its sequel, we study the braid indices for all non-alternating pretzel links by a systematic approach. Pretzel links can be divided into three types according to the Seifert circle decompositions of their standard link diagrams. In this paper, we present our results on Type 1 and Type 2 pretzel links, namely the complete formulation of the braid indices for all non-alternating Type 1 and Type 2 pretzel links. Since the braid indices are already known for all alternating pretzel links from our previous work, it means that we have now completely determined the braid indices for all Type 1 and Type 2 pretzel links. [ABSTRACT FROM AUTHOR]