{"paper":{"title":"An annihilation-number Caro-Wei bound: a TxGraffiti conjecture and an independence-number bracket","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Chakshu Gupta","submitted_at":"2026-06-28T18:36:06Z","abstract_excerpt":"Automated conjecturing programs scan collections of graphs for inequalities between invariants that no stored graph violates, then offer the survivors for proof or refutation. TxGraffiti, one such program, conjectured that every nontrivial connected graph $G$ satisfies $\\alpha(G) \\ge \\bigl(a(G) + R(G)\\bigr)/\\Delta(G)$, where $\\alpha$ is the independence number, $a$ the annihilation number, $R$ the residue, and $\\Delta$ the maximum degree. Established only for two special families of graphs, the conjecture has otherwise remained open. The note proves the degree-sequence inequality $a \\le \\tfrac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29553","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/2606.29553/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"}