Geometric Graphs with Unbounded Flip-Width

TL;DR

This paper investigates the flip-width property of various geometric graphs, establishing that many such graphs have unbounded flip-width, which impacts their structural and algorithmic understanding.

Contribution

It proves that numerous classes of geometric graphs possess unbounded flip-width, extending the understanding of their structural complexity.

Findings

Many geometric graph classes have unbounded flip-width.

Unbounded flip-width applies to interval, permutation, circle, and other geometric graphs.

Implications for algorithms and structural analysis of these graphs.

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.