Bicolouring Steiner triple systems (Colbourn–Dinitz–Rosa product, Dinitz–Stinson conditions)
Source: github.com/jtraverso/cdr-bicolouring-sts/tree/a768a98a648e9…
A Lean 4 / Mathlib formalization of the product theorem of Colbourn, Dinitz and Rosa for bicoloured Steiner triple systems and of the necessary conditions of Dinitz and Stinson. A bicolouring of an STS colours the points so that every block receives exactly two colours. bicolourable3_mul (CDR 1999, Theorem 2.4): if there is an (a, b, c)-bicolourable STS(u) with c = max(a, b, c) and c ≤ a + b, and an (x, y, z)-bicolourable STS(v), then there is an (ax + by + cz, ay + bz + cx, az + bx + cy)-bicolourable STS(uv). Dinitz–Stinson Proposition 1.2: for a bicoloured STS on v points with colour…
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