{"paper":{"title":"A note on Ordered Ruzsa-Szemer\\'edi graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DS","authors_text":"Kevin Pratt","submitted_at":"2025-02-04T16:21:02Z","abstract_excerpt":"A recent breakthrough of Behnezhad and Ghafari [FOCS 2024] and subsequent work of Assadi, Khanna, and Kiss [SODA 2025] gave algorithms for the fully dynamic $(1-\\varepsilon)$-approximate maximum matching problem whose runtimes are determined by a purely combinatorial quantity: the maximum density of Ordered Ruzsa-Szemer\\'edi (ORS) graphs. We say a graph $G$ is an $(r,t)$-ORS graph if its edges can be partitioned into $t$ matchings $M_1,M_2, \\ldots, M_t$ each of size $r$, such that for every $i$, $M_i$ is an induced matching in the subgraph $M_{i} \\cup M_{i+1} \\cup \\cdots \\cup M_t$. This is a r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.02455","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/2502.02455/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"}