Fractional triangle decompositions of dense tripartite graphs
A Lean 4 / Mathlib formalization of the main results of Allsop, Bowtell, Lesgourgues and Petrova, "Improved bounds on completion of partial Latin squares" (arXiv:2609.37877, 2026): there is η > 0 (here η = 1/20000) such that every K₃-divisible spanning subgraph of K_{n,n,n} with minimum partite degree at least (0.769 − η)n has a fractional triangle decomposition (Theorem 1.3). Also formalized: the Farkas characterization (Lemma 2.1); the reduction to triangle-covered, balanced, untied and nonzero edge weightings (Proposition 3.1, Corollary 3.5), with Lemma 3.4 proved through an integral…
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