ER-completeness of segment visibility graph recognition

Ascertain whether the recognition problem for segment visibility graphs (graphs defined by line-of-sight among segments with segments acting as obstacles) is ER-complete.

Background

Segment visibility graphs consider segments as both entities and obstacles; recognition asks whether a given graph arises from such visibility relations.

Despite significant progress on related visibility graph problems, the authors indicate that the ER-completeness status for segment visibility graphs is unresolved.