Faster recognition of quasi-triangulated graphs via decremental simplicial-vertex maintenance

Determine whether Triangle Detection, Simplicial Vertex, and high-dimensional Orthogonal Vectors retain n^{\omega}-time algorithms in the decremental setting relevant to recognizing quasi-triangulated graphs, or whether a fine-grained complexity separation emerges among these problems.

Background

A quasi-triangulated graph can be recognized by repeatedly removing a simplicial or cosimplicial vertex, which leads to a decremental simplicial-vertex subroutine. The paper improves the running time of this subroutine but does not establish an n^{\omega}-time algorithm. It explicitly identifies as unresolved whether the relevant problems—Triangle Detection, Simplicial Vertex, and high-dimensional Orthogonal Vectors—share n^{\omega}-time complexity or exhibit a meaningful difference.