On the crossing numbers of certain generalized Petersen graphs (Q1198516)

The authors give a short proof of the fact that the generalized Peterson graph \(P(8,3)\) has crossing number 4 and that the crossing number of \(P(10,3)\) is at least five (contrary to a claim by \textit{S. Fiorini} [Combinatorics '84, Proc. Int. Conf. Finite Geom. Comb. Struct., Bari/Italy 1984, Ann. Discrete Math. 30, 225-241 (1986; Zbl 0595.05030)]). The method is interesting in that it focuses on disjoint cycles which must cross each other an even number of times.