{"paper":{"title":"k-Planar and Fan-Crossing Drawings and Transductions of Embeddable Graphs","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.LO","math.CO"],"primary_cat":"cs.CG","authors_text":"Jan Jedelsk\\'y, Petr Hlin\\v{e}n\\'y","submitted_at":"2025-06-10T08:54:08Z","abstract_excerpt":"We introduce, for every surface $\\Sigma$, a two-way connection between definability of a graph class $\\mathcal C$ by FO transductions (first-order logical transformations) of the graphs embeddable in $\\Sigma$ and a certain variant of fan-crossing drawings of the graphs from $\\mathcal C$ in $\\Sigma$. If the considered class $\\mathcal C$ is additionally of bounded maximum degree, then the restriction on drawings of the graphs from $\\mathcal C$ in $\\Sigma$ is simply to have a bounded number of crossings per edge (such as being $k$-planar for fixed~$k$ if $\\Sigma$ is the plane). For graph classes,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08585","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.08585/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}