Lax Lean Archive

Proof of `Independent Set Reduces to Multicoloured Clique` (1st statement)

groundedproofs/Lax496464Proofs/WHierarchy/MccNP/CorrectnessProof.lean · lax-496464

What this proof establishes

no assumptions

thm✓Lax496464.WH_F4_IndependentSetToMcc (1st 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

GG has an independent set of size at least kk if and only if its multicoloured graph has a multicoloured clique: the copies (c,vc)(c, v_c) of kk pairwise different, pairwise non-adjacent vertices form one, and conversely the vertices of a multicoloured clique are such a family.