Universal Rigidity of Ladders on the line

Abstract: In "Universal rigidity on the line, point orde" it is shown, answering a question of Jord\'an and Nguyen, that universal rigidity of a generic bar-joint framework in R^1 depends on more than the ordering of the vertices. The graph G that was used in that paper is a ladder with three rungs. Here we provide a general answer when that ladder with three rungs in the line is universally rigid and when it is not.