2026-07-22T11:41:37Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:25037 2026-02-09T07:53:58Z ddc:004 open_access

Graph Tiles (Poster Abstract) Aichholzer, Oswin Ganian, Robert Keldenich, Phillip Löffler, Maarten Meijer, Gert Weinberger, Alexandra Wenk, Carola graph tiles 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Oswin Aichholzer and Robert Ganian and Phillip Keldenich and Maarten Löffler and Gert Meijer and Alexandra Weinberger and Carola Wenk 2025 Is Part Of LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.GD.2025.51 urn:nbn:de:0030-drops-250371 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.51 eng https://creativecommons.org/licenses/by/4.0/legalcode