{"id":"hexagon/2610.00501","pdf":"https://hexagonmath.org/pdf/2610.00501v1","url":"https://hexagonmath.org/abs/2610.00501v1","tags":["msc:05C69","msc:05C05","msc:05C07","Graffiti.pc","complement","counterexample","degree sequence","forest number","induced forest"],"score":0,"title":"A counterexample to a conjecture of Graffiti.pc on the forest number","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Deep Bhattacharjee"],"reviews":0,"subject":"math.CO","summary":"Conjecture 66 of Graffiti.pc bounds the order of a largest induced forest of a connected graph from below by the even mode of the degrees of its complement divided by its average degree. We show that it is false, under every reading of its definitions and by an unbounded margin.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Code"],"discussed":0,"published":"2026-10-23","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}