Linear-error clique partitions of split graphs
A Lean 4 / Mathlib formalization of the main results of the author's preprint "Linear-Error Clique Partitions of Split Graphs via Structured Triangle Packing" (Erdős #81 series, Paper III): there is an absolute constant C such that every finite split graph G on n vertices satisfies |E(G)| − 2ν₃(G) ≤ n²/6 + C·n, where ν₃(G) is the maximum number of pairwise edge-disjoint triangles (Theorem 1.1); consequently G has a clique partition (a family of cliques covering every edge exactly once) with at most n²/6 + C·n cliques (Corollary 1.2). The quadratic coefficient 1/6 is the sharp one for split…
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