Beaudou, Laurent; Dorbec, Paul; Gravier, Sylvain; Jha, Pranava K. On planarity of direct product of multipartite complete graphs. (English) Zbl 1173.05315 Discrete Math. Algorithms Appl. 1, No. 1, 85-104 (2009). 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. Cited in 2 Documents MSC: 05C10 Planar graphs; geometric and topological aspects of graph theory 05C83 Graph minors Keywords:direct product; planarity; complete graph; multipartite complete graph; subdivision PDFBibTeX XMLCite \textit{L. Beaudou} et al., Discrete Math. Algorithms Appl. 1, No. 1, 85--104 (2009; Zbl 1173.05315) Full Text: DOI References: [1] DOI: 10.4153/CMB-1969-015-9 · Zbl 0177.52402 · doi:10.4153/CMB-1969-015-9 [2] DOI: 10.1016/S0020-0190(98)00145-8 · Zbl 1339.05338 · doi:10.1016/S0020-0190(98)00145-8 [3] DOI: 10.4153/CJM-1977-027-1 · Zbl 0343.18004 · doi:10.4153/CJM-1977-027-1 [4] Imrich W., Product Graphs: Structure and Recognition (2000) [5] Jha P. K., Zastos. Mat. (Applic. Math.) 21 pp 537– [6] Kuratowski K., Fund. Math. 15 pp 271– [7] Wagner K., Duet. Math. 2 pp 280– This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.