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Proof of `Twin-width is bounded by a function of mixed minor number`
groundedproofs/Lax49Proofs/TwinWidthFromMixedMinorNumber.lean · lax-49
What this proof establishes
no assumptions
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
Twin-width (the parameter of submission Lax48) is bounded by a numerical function of the submitted mixed minor number.
Proof strategy
The source direction is the mirrored Boolean Theorem 14 construction: an ordered adjacency matrix of mixed number is -mixed-free, and the Marcus–Tardos-based Theorem 10 machinery turns a mixed-free matrix into a contraction sequence of bounded red degree. Rewriting with the two parameter equalities of moves the bound onto the submitted parameters, with the same witness function.
Attribution
Bonnet, Kim, Thomassé and Watrigant, Twin-width I: Tractable FO Model Checking (J. ACM 2022).