Work

Deciding monotonicity of simple drawings of the complete graph

Year: 2026

Type: article

Abstract: A drawing of a graph is $x$-monotone if every vertical line intersects each edge of the graph at most once. We present an $O(n^5)$ time algorithm for deciding whether a simple drawing of the complete graph $K_n$ is weakly isomorphic to an $x$-monotone drawing. We note that this algorithm can also decide whether a drawing of $K_n$ is strongly isomorphic to an $x$-monotone drawing.

Source: Journal of computational geometry

DOI: 10.20382/jocg.v17i1a11

Authors: Aichholzer, Oswin, Hackl, Thomas, Pilz, Alexander, Salazar, Gelasio, Vogtenhuber, Birgit

Institutions: Graz University of Technology, Autonomous University of San Luis Potosí

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: Austrian Science Fund, European Social Fund

Awards: EuroGIGA_Erdös-Szekeres type problems for colored point sets and compatible graphs, G8381026457, Combinatorial problems on geometric graphs