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ER-Completeness of Segment Visibility Graphs

Determine whether the recognition problem for segment visibility graphs is ER-complete.

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Background

Segment visibility graphs have vertices representing segments and edges denoting mutual visibility of segments via unobstructed line-of-sight.

The survey notes NP-hardness results for related visibility settings but explicitly states that ER-completeness of segment visibility graph recognition is unresolved.

References

It is also not clear whether segment visibility graphs are -complete.

— The Existential Theory of the Reals as a Complexity Class: A Compendium (2407.18006 - Schaefer et al., 25 Jul 2024) in Section “Visibility Graphs”