Lax Lean Archive

Proof of `Multicoloured Clique Is W[1]-Complete` (3rd statement)

groundedproofs/Lax496464Proofs/WHierarchy/Reductions/CliqueMCC/ForgetFinal.lean · lax-496464

What this proof establishes

thm✓Lax496464.WH_D12_MulticolouredClique (3rd statement)

Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.

Read the Lean proof on GitHub

Description

Multicoloured Clique ≤fpt p-Clique. Forget the colours: the word keeps its graph block and its last entry, the number of colours. A clique of kk vertices in a properly kk-coloured graph has one vertex of each colour, and a multicoloured clique is a kk-clique; the parameter is unchanged, and the map is computed in linear time.