On planarity of direct product of multipartite complete graphs
Résumé
The planarity of the direct product of two graphs has been widely studied in the past. Surprisingly, the missing part is the product with $K_2$, which seems to be less predictible. In this piece of work, we characterize which subdivisions of multipartite complete graphs, have their direct product with $K_2$ planar. This can be seen as a step towards the characterization of all such graphs.
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