Graph Tiles (Poster Abstract)

Aichholzer, Oswin; Ganian, Robert; Keldenich, Phillip; Löffler, Maarten; Meijer, Gert; Weinberger, Alexandra; Wenk, Carola

doi:10.4230/LIPIcs.GD.2025.51

Abstract

We define a graph tile to be a unit square (or more generally, a polygon) on which a piece of a graph has been drawn/embedded; in particular, it may have vertices in its interior, edges connecting those vertices, or half-edges that extend to the boundary of the tile. In a graph tiling problem, we are given as input a set of graph tiles, with multiplicities, and the output is an arrangement of those tiles forming a graph of larger area. We focus on a simple tile set: unit square tiles with a central vertex and either a half-edge or no half-edge on each side. Up to symmetry this gives us six different types. We characterize which multiplicities are compatible for sets of at most three different tiles.

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Oswin Aichholzer, Robert Ganian, Phillip Keldenich, Maarten Löffler, Gert Meijer, Alexandra Weinberger, and Carola Wenk. Graph Tiles (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 51:1-51:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.GD.2025.51

Author Details

Oswin Aichholzer

TU Graz, Austria

Robert Ganian

TU Wien, Austria

Phillip Keldenich

TU Braunschweig, Germany

Maarten Löffler

Utrecht University, The Netherlands

Gert Meijer

Stenden University of Applied Sciences, Leeuwarden, The Netherlands

Alexandra Weinberger

FernUniversität in Hagen, Germany

Carola Wenk

Tulane University, New Orleans, LA, USA

Acknowledgements

This research was initiated at Dagstuhl Seminar 25201, "Computational Geometry". We thank the organizers and all participants for a stimulating atmosphere and valuable discussions. This research was made possible by the Centre for Unusual Collaborations (CUCo) under the project "Going Off the Grid".

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Graph Tiles (Poster Abstract)

Authors Oswin Aichholzer , Robert Ganian , Phillip Keldenich , Maarten Löffler , Gert Meijer , Alexandra Weinberger , Carola Wenk

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