On the crossing numbers of certain generalized Petersen graphs

Abstract

In his paper on the crossing numbers of generalized Peterson graphs, Fiorini proves that P(8,3) has crossing number 4 and claims at the end that P(10, 3) also has crossing number 4. In this article, we give a short proof of the first claim and show that the second claim is false. The techniques are interesting in that they focus on disjoint cycles, which must cross each other an even number of times.