{"paper":{"title":"Graph Parameters, Universal Obstructions, and WQO","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Christophe Paul, Dimitrios M. Thilikos, Evangelos Protopapas","submitted_at":"2023-04-07T15:14:22Z","abstract_excerpt":"We establish a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering $\\leqslant$ on graphs. At the center of this framework lies the concept of a $\\leqslant$-parametric graph: a non $\\leqslant$-decreasing sequence $\\mathscr{G} = \\langle \\mathscr{G}_{t} \\rangle_{t \\in \\mathbb{N}}$ of graphs indexed by non-negative integers. Parametric graphs allow us to define combinatorial objects that capture the approximate behaviour of graph parameters. A finite set $\\mathfrak{G}$ of $\\leqslant$-parametric graphs is a $\\leqslant$-universal obst"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.03688","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/2304.03688/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"}