In conferences held at the Oberwolfach Institute, participants usually dine together in a room witg tables of different sizes, and each participant has an assigned seat. Gerhard Ringel asked whether there exists a seating arrangement for an odd number $$v$$ of people and $$\frac{v-1}{2}$$ meals so that all pairs of participants are seated next to each other exactly once.

In short, don't leave your next night with friends to chance. Do an exact 2-factorization before taking seats for a beer!

The full pre-print is available on Arxiv at this link.

###### Resources
• gitHub repository for the OberSolver
• gitHub repository for the general Oberwolfach Solver
• gitHub repository for the proof of $$OP(^23,5)$$
###### Combinatorial Mysteries

For the specific case of $$OP(^23,5)$$, is likely that no solution exists. Despite this fact, apparently no proof (either computational or analytical) has been published.

All the references loop around this, and this. Finally, here Piotrowski says the non-existence has been proven with a computer calculation around the 80s, and the result is safely stored inside an unpublished paper in German.

Well, thanks to Integer Programming there is now a citable proof :)

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