Written on the Wall II Conjecture 109

Conjecture 109 in Written on the Wall II proposes a universal graph bound involving independence number, largest induced bipartite subgraph and Havel–Hakimi residue. The recorded test graph joins an independent seven-vertex set to two disjoint triangles.

Why it matters and what counts as progress

Why it matters: A finite witness can separate three graph invariants linked by the proposed universal inequality.

What counts as progress: An exact computation giving independence number 7, largest induced bipartite order 9 and residue 2, contradicting the proposed bound 6, or a corrected universally valid inequality.

How the problem developed

17 Aug 2026 · Counterexample [1][2]
Andrii Vlasenko, with GPT-5.6 Sol Max Released an explicit 13-vertex connected graph with independence number 7, largest induced bipartite subgraph order 9 and Havel–Hakimi residue 2, violating the proposed bound of 6.

AI contribution

AI-found graph refutes Written on the Wall II Conjecture 109

A connected 13-vertex graph formed by joining an independent seven-vertex set to two disjoint triangles has independence number 7, largest induced bipartite subgraph size 9 and Havel–Hakimi residue 2. These values violate Conjecture 109’s proposed bound of 6.

AI involvementAI-led

ImportanceModest

Technical verificationFormal (Lean 4 and exact exhaustive computation)

Human understandingFew