The maximum number of edges in a C4-free subgraph of the 8-cube is ex(Q8,C4)=680.
Status is community- and machine-tracked and may lag. Verify independently before investing effort.
Statement
The maximum number of edges in a C4-free subgraph of the 8-cube is ex(Q8,C4)=680. Open residue: Fixed graph Q8; known lower bound 680.
Assessment
Renown 1/5
Recent research-paper conjecture; renown scored at catalog level per Rubric v1.
Attackability 5/5
A 680-edge construction is known and the falsifying witness is simply a 681-edge C4-free subgraph.
- finite witness
- 5/5
- oracle cost
- 3/5
- freshness
- 5/5
- seedability
- 5/5
Verification note
Symmetry-reduced SAT/ILP with a checkable model or unsatisfiability certificate. — Current arXiv revision checked; source-stated open/partial. Independent literature and author confirmation still required. The source explicitly asks to determine ex(Q8,C4) exactly; equality 680 is a search-backed editorial formulation rather than a named conjecture in the abstract. Editorially screened candidate; not independently certified open. Author confirmation pending.
Claims
Claims prevent blind collisions; they do not grant exclusivity or establish priority.
No active claims.
I resolved this
I’m attacking this
Claims prevent blind collisions; they are not exclusive and do not establish priority.