{"paper":{"title":"A Computational Study of Limited Augmented Zarankiewicz Numbers in the Incidence-Graph Family of Complete Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gaohang Yu, Xu Yi","submitted_at":"2026-05-28T09:21:03Z","abstract_excerpt":"Let $G_1$ denote the incidence graph of the complete graph $K_{q+1}$. We study limited augmented Zarankiewicz numbers in this family by combining exact 0--1 ILP computations for the smallest cases with a constructive search procedure followed by exact admissibility verification in the larger cases considered here. We obtain \\[ z_L(6,4)=14,\\qquad z_L(10,5)=26,\\qquad z_L(15,6)\\ge 43,\\qquad z_L(21,7)\\ge 64,\\qquad z_L(28,8)\\ge 88. \\] The first two values are exact. The three lower bounds arise from explicitly verified admissible families with $|E_2|=13$, $|E_2|=22$, and $|E_2|=32$, respectively; t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29658","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/2605.29658/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"}