Geodesic
A proof of the crossing number of $K_{3,n}$ in a surface
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 549-551 Cet article a éte moissonné depuis la source Library of Science

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In this note we give a simple proof of a result of Richter and Siran by basic counting method, which says that the crossing number of K_3,n in a surface with Euler genus ε is
Keywords: crossing number, bipartite graph, surface 
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Ho, Pak. A proof of the crossing number of $K_{3,n}$ in a surface. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 549-551. http://geodesic.mathdoc.fr/item/DMGT_2007_27_3_a10/

[1] R.K. Guy and T.A. Jenkyns, The toroidal crossing number of $K_{m,n}$, J. Combin. Theory 6 (1969) 235-250, doi: 10.1016/S0021-9800(69)80084-0.

[2] R.B. Richter and J. Siran, The crossing number of $K_{3,n}$ in a surface, J. Graph Theory 21 (1996) 51-54, doi: 10.1002/(SICI)1097-0118(199601)21:151::AID-JGT7>3.0.CO;2-L

[3] G. Ringel, Das Geschlecht des vollständigen paaren Graphen, Abh. Math. Sem. Univ. Hamburg 28 (1965) 139-150, doi: 10.1007/BF02993245.

[4] G. Ringel, Der vollständige paare Graph auf nichtorientierbaren Flächen, J. Reine Angew. Math. 220 (1965) 88-93, doi: 10.1515/crll.1965.220.88.