{"paper":{"title":"Edge-Number Bounds for the Inversion Diameter of Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anqi Li, Jiawen Bo, Xiaopan Lian, Xin Yan","submitted_at":"2026-06-16T14:28:59Z","abstract_excerpt":"The inversion of a set $X$ of vertices in an oriented graph reverses every arc with both endpoints in $X$. The inversion graph $I(G)$ of a graph $G$ has the labelled orientations of $G$ as its vertices, two orientations being adjacent when a single inversion transforms one into the other, and the inversion diameter $\\diam(I(G))$ is its diameter. Answering a question of Havet, H\\\"orsch and Rambaud, we prove the bound in terms of edge number $\\diam(I(G)) \\le 2\\sqrt{|E(G)|}$, and we complement it with a lower bound $\\diam(I(G)) \\ge \\frac{|E(G)|}{|V(G)|}$ obtained by viewing $I(G)$ as a Cayley gra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17974","kind":"arxiv","version":1},"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/2606.17974/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"}