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On planarity of direct product of multipartite complete graphs. (English) Zbl 1173.05315

Summary: 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.

MSC:

05C10 Planar graphs; geometric and topological aspects of graph theory
05C83 Graph minors
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