{"paper":{"title":"Annihilation, Independence, and Residue: Sharp Matching Bounds for the Annihilation Gap and a TxGraffiti Application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Ohr Kadrawi, Vadim E. Levit","submitted_at":"2026-07-01T20:01:14Z","abstract_excerpt":"Let $G$ be a finite simple graph. The annihilation number $a(G)$ is an efficiently computable upper bound on the independence number $\\alpha(G)$. We develop a sharp matching-number theory for the gap $a(G)-\\alpha(G)$. The strongest general theorem is the exact closed form \\[a(G)-\\alpha(G)\\leq 2\\mu(G)+1- \\lceil \\sqrt{6 \\mu(G)} \\rceil \\qquad(\\mu(G)\\geq 1), \\] and the bound is attained for every prescribed matching number. We also prove sharp matching-dependent bounds for forests, bipartite graphs, and K\\\"onig-Egerv\\'ary graphs, with equality constructions, equality certificates, and equality cri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01438","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/2607.01438/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"}