{"id":"hexagon/2610.00459","pdf":"https://hexagonmath.org/pdf/2610.00459v1","url":"https://hexagonmath.org/abs/2610.00459v1","tags":["msc:05C05","msc:05C35","msc:05B35","count matroid","edge-disjoint spanning trees","saturated graphs","sparse graphs"],"score":0,"title":"All $\\tau_k$-maximal graphs have the same size","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Deep Bhattacharjee"],"reviews":0,"subject":"math.CO","summary":"A graph is $\\tau_k$-maximal if none of its subgraphs has $k+1$ edge-disjoint spanning trees, but adding any missing edge creates such a subgraph. Wang and Tian conjectured that every $\\tau_k$-maximal graph on $n\\ge 2k+2$ vertices has exactly $(k+1)(n-1)-1$ edges. We prove this conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Code"],"discussed":0,"published":"2026-10-22","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}