Triangle decompositions of dense tripartite graphs and completion of partial Latin squares
A Lean 4 / Mathlib formalization of Corollary 1.6 for r = 3 of Barber, Kühn, Lo, Osthus and Taylor, "Clique decompositions of multipartite graphs and completion of Latin squares" (J. Combin. Theory Ser. A 151 (2017), arXiv:1603.01043): fractional triangle decompositions above a threshold give triangle decompositions above the same threshold. Precisely: if δ ≥ 3/4 and, for every ε > 0, every K₃-divisible tripartite graph with three parts of size n ≥ n₀(ε) and minimum partite degree at least (δ + ε)n has a fractional triangle decomposition, then for every ε > 0 there is n₀ such that every…
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