{"paper":{"title":"Dual Cheeger constant for weighted graphs over ordered fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.CO","authors_text":"Anna Muranova","submitted_at":"2022-11-03T08:54:59Z","abstract_excerpt":"We consider a dual Cheeger constant $\\overline h$ for finite graphs with edge weights from an arbitrary real-closed ordered field. We obtain estimates of $\\overline h$ in terms of number of vertices in graph. Further, we estimate the largest eigenvalue for the discrete Laplace operator in terms of $\\overline h$ and show the sharpness of estimates. As an example we consider graphs over non-Archimedean field of the Levi-Civita numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.01654","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/2211.01654/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"}