Gethner–Sulanke 19-vertex biplanar graph question
Does there exist a biplanar graph such that and ? Here, biplanar means that can be partitioned into the edge sets of two planar graphs on the common vertex set .
References
Primary source
Additional references
- Biplanar graphs with independence number two are 9-colorable — arXiv — Stefan Szeider
Progress summary
A new computer-checked argument claims the proposed -vertex graph cannot exist, but independent confirmation is not recorded.
The question asks whether a proposed -vertex biplanar graph configuration exists. The retrieved material reports a negative answer via structural reduction and exhaustive computation.
September 2026 development
Stefan Szeider's paper Biplanar graphs with independence number two are -colorable reports that a structural reduction and certified SAT enumeration exclude the proposed configuration. The computation is reported as checked in Lean , so the result would settle the question negatively; this claim remains unverified.
Current status (as of September 2026): The proposed -vertex configuration is claimed impossible, but the reported computational proof has not been independently verified.
Solutions 0
No solutions have been posted yet.