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On the crossing numbers of certain generalized Petersen graphs. (English) Zbl 0756.05048

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 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.

MSC:

05C10 Planar graphs; geometric and topological aspects of graph theory
05C99 Graph theory

Citations:

Zbl 0595.05030
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References:

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