Strongly almost trivial theta-curves

Abstract

A theta-curve is called almost trivial if it does not contain any non-trivial knot. A theta-curve is called strongly almost trivial if it has a planar projection which does not contain a projection of any non-trivial knot. In this paper, we introduce a method to present strongly almost trivial theta-curves. We also give an almost trivial theta-curve which may not be strongly almost trivial.