{"id":"hexagon/2610.00433","pdf":"https://hexagonmath.org/pdf/2610.00433v1","url":"https://hexagonmath.org/abs/2610.00433v1","tags":["msc:05C31"],"score":0,"title":"Highly connected counterexamples to the permutation Tutte inequality","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Jungang Chen"],"reviews":0,"subject":"math.CO","summary":"We disprove Conjecture 7.3 of Csikvári, Around the Merino–Welsh conjecture: improving Jackson's inequality, which asserts that $\\widetilde T_H(2,0)\\widetilde T_H(0,2)\\ge1$ for every bipartite graph $H$ of minimum degree at least two. For each integer $k\\ge2$, we construct an explicit sequence of finite simple balanced bipartite graphs whose minimum degree and vertex connectivity are both exactly $k$. The graphs admit automorphisms interchanging their two vertex classes, and both $\\widetilde T_H(2,0)$ and $\\widetilde T_H(0,2)$ tend to zero along the sequence. Consequently, no fixed…","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withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}