{"paper":{"title":"An improved upper bound on the oriented diameter of graphs with diameter $4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Every bridgeless graph with diameter 4 admits a strong orientation whose diameter is at most 18.","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jifu Lin, Lihua You, Xiaolin Wang","submitted_at":"2026-05-12T07:27:23Z","abstract_excerpt":"Let $f(d)$ be the smallest value for which every bridgeless graph $G$ with diameter $d$ admits a strong orientation $\\overrightarrow{G}$ such that the diameter of $\\overrightarrow{G}$ is at most $f(d)$. Chv\\'atal and Thomassen (JCTB, 1978) established general bounds for $f(d)$, and also proved that $f(2)=6$ and $f(4)\\geq 12$. The works of both Kwok, Liu and West (JCTB, 2010) and Wang and Chen (JCTB, 2022) together determined $f(3)=9$. In this paper, we improve the best known upper bound for $f(4)$ from $21$ (Babu et al., DAM, 2021) to \\textbf{$18$}."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"In this paper, we improve the upper bound of f(4) to 18.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The proof relies on the existence of a specific orientation construction that achieves diameter 18 for arbitrary bridgeless diameter-4 graphs; if the case analysis or reduction steps in the full proof contain an uncovered configuration, the bound fails.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The oriented diameter function satisfies f(4) ≤ 18, improving the prior upper bound of 21.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Every bridgeless graph with diameter 4 admits a strong orientation whose diameter is at most 18.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"28069256f68656cc8377e7fb4932a7ea9791d0def986aba474f3b25f476818c0"},"source":{"id":"2605.11667","kind":"arxiv","version":2},"verdict":{"id":"a47325b5-1d86-44f7-b2f8-fe47eeae0e3d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T01:02:55.682612Z","strongest_claim":"In this paper, we improve the upper bound of f(4) to 18.","one_line_summary":"The oriented diameter function satisfies f(4) ≤ 18, improving the prior upper bound of 21.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The proof relies on the existence of a specific orientation construction that achieves diameter 18 for arbitrary bridgeless diameter-4 graphs; if the case analysis or reduction steps in the full proof contain an uncovered configuration, the bound fails.","pith_extraction_headline":"Every bridgeless graph with diameter 4 admits a strong orientation whose diameter is at most 18."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.11667/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-21T00:01:32.372051Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-20T14:07:13.565330Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-20T03:42:00.549097Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T11:40:12.294538Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"5bd2b1cd68e44bb960105db05ea4c79b06b7c7fa7730e1575ba44086bf2b13f9"},"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"}