{"id":"hexagon/2610.00431","pdf":"https://hexagonmath.org/pdf/2610.00431v1","url":"https://hexagonmath.org/abs/2610.00431v1","tags":["msc:05C31"],"score":0,"title":"Counterexamples to Three Conjectures of Ok on Tutte-Polynomial Deletion Ratios","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Jungang Chen"],"reviews":0,"subject":"math.CO","summary":"We disprove Conjectures 7.2.1, 7.2.2, and 7.2.3 from Seongmin Ok's thesis *Aspects of the Tutte Polynomial*. Conjecture 7.2.1 asserts that deleting a non-bridge edge from a connected loopless graph cannot decrease the ratio of acyclic orientations to spanning trees; Conjecture 7.2.2 strengthens this to monotonicity of T_{G-e}(x,2-x)/T_G(x,2-x) on 0 ≤ x ≤ 2. Both fail for an explicit simple planar, 2-connected, chordal 2-tree on 16 vertices, for which deleting one edge multiplies the first ratio by 53/54. A two-parameter construction gives an exact criterion for infinitely many…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT"],"discussed":0,"published":"2026-10-21","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}