Near-regular hypergraph matchings and the asymptotic triangle-packing gap
A Lean 4 / Mathlib formalization of three results. (1) A finite nibble theorem: r-uniform hypergraphs whose degrees are at most (1+μ)d everywhere and at least (1−μ)d outside an exceptional set of at most η|V| vertices, with codegrees at most μd, have matchings with at least (1−β)|V|/r edges. (2) The fractional–integral triangle-packing gap is o(n²) uniformly over finite graphs: every large graph has an edge-disjoint triangle family P such that every fractional triangle packing has weight at most |P| + εn² (the triangle case of Haxell–Rödl). (3) The cover form: a fractional triangle cover of…
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