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We investigate some algebraic structures called quasi-trivial quandles and weuse them to study link-homotopy of pretzel links. Precisely, a necessary andsufficient condition for a pretzel link with at least two components beingtrivial under link-homotopy is given. We also generalize the quasi-trivialquandle idea to the case of biquandles and consider enhancement of thequasi-trivial biquandle cocycle counting invariant by quasi-trivial biquandlecocycles, obtaining invariants of link-homotopy type of links analogous to thequasi-trivial quandle cocycle invariants in Ayumu Inoue's articlearXiv:1205.5891.

Quasi-trivial Quandles and Biquandles, Cocycle Enhancements and Link-Homotopy of Pretzel links