Work

Representing Hypergraphs by Point-Line Incidences

Year: 2026

Type: article

Abstract: We consider hypergraph visualizations that represent vertices as points in the plane and hyperedges as curves passing through the points of their incident vertices. Specifically, we consider several different variants of this problem by (a) restricting the curves to be lines or line segments, (b) allowing two curves to cross if they do not share an element, or not; and (c) allowing two curves to overlap or not. We show $\exists\mathbb{R}$-hardness for six of the eight resulting decision problem variants and describe polynomial-time algorithms in some restricted settings. Lastly, we briefly touch on what happens if we allow the lines of the represented hyperedges to have bends - to this we generalize a counterexample to a long-standing result that was sometimes assumed to be correct. 24 pages, 12 figures

Source: Discrete Mathematics & Theoretical Computer Science

DOI: 10.46298/dmtcs.15876

Authors: Alexander Dobler, Stephen Kobourov, Debajyoti Mondal, Martin Nöllenburg

Institutions: TU Wien, Technical University of Munich, University of Saskatchewan

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: Vienna Science and Technology Fund, Natural Sciences and Engineering Research Council of Canada

Awards: G5259471551, G5528860119