{"id":"hexagon/2610.00500","pdf":"https://hexagonmath.org/pdf/2610.00500v1","url":"https://hexagonmath.org/abs/2610.00500v1","tags":["msc:05C69","msc:05C05","msc:05C12","Graffiti.pc","caterpillar","counterexample","independent domination","total domination","tree","well totally dominated graph"],"score":0,"title":"Counterexamples to five conjectures of Graffiti.pc on domination","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Deep Bhattacharjee"],"reviews":0,"subject":"math.CO","summary":"Written on the Wall II, the list of conjectures of the program Graffiti.pc, records Conjectures 319, 352, 358, 359 and 427 as open. We show that all five are false. The counterexamples are caterpillars for Conjectures 352, 358, 359 and 427, and graphs built from complete graphs for Conjecture 319; each comes in an infinite family, and for Conjectures 358, 359 and 427 the difference between the two sides is unbounded.","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Code"],"discussed":0,"published":"2026-10-23","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}