Geometric Graphs with Unbounded Flip-Width

Abstract

We consider the flip-width of geometric graphs, a notion of graph width recently introduced by Toru\'nczyk. We prove that many different types of geometric graphs have unbounded flip-width. These include interval graphs, permutation graphs, circle graphs, intersection graphs of axis-aligned line segments or axis-aligned unit squares, unit distance graphs, unit disk graphs, visibility graphs of simple polygons, $\beta$-skeletons, 4-polytopes, rectangle of influence graphs, and 3d Delaunay triangulations.