{"schema":"vela.problem-packet.v0.1","problem":23,"statement":"Can every triangle-free graph on $5n$ vertices be made bipartite by deleting at most $n^2$ edges?","status":"open","seam":"sealed","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[{"id":"att_767389b4c2a3ad54","kind":"known_result","claim":"FULL ERDOS AUDIT (workflow wf_de3c1580): of 430 ingested problems, the 72 shape-promising ones deeply audited (live status+comments, anti-confab) -> 91 assessed, ALL disqualified except #23. Corpus essentially EXHAUSTED for Vela-solvable targets. The lone fresh target is #23's finite Lean test-sorries (n=1 case on 5-vertex graphs + C5 tightness witness + blowupC5_tight counting lemma).","grade":"extends_prior_work","gateStatus":"needs_verification","superseded":false}],"velaLean":[],"oeis":[{"id":"A389646","name":"Maximum number of edges that need to be removed from a triangle-free graph on n vertices to make it bipartite.","terms":"0,0,0,0,1,1,1,2,2,4,4,5,6,7,9,9,10,12,13,16,16,17,20","url":"https://oeis.org/A389646"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}