Lax Lean Archive

Draft — mutable and not usable as a dependency; its citation marks the draft state.

Proof of `Erdős–Hajnal theorem for the five-cycle`

groundedproofs/Lax54Proofs/Main.lean · lax-54

What this proof establishes

thm✓Lax54.ErdosHajnalC5

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

Proof of Theorem 4.4. Strong induction reduces the result to a critical counterexample. The critical-comb statement and the induced-C5C_5 obstruction between distinct blocks exclude that case. Finally, κ(G)=α(G)ω(G)≤h(G)2\kappa(G)=\alpha(G)\omega(G)\leq h(G)^2 gives the asserted exponent.