Fulkerson’s Conjecture and Loupekine snarks

In 1976, F. Loupekine created a method for constructing new snarks from already known ones. In the present work, we consider an infinite family of Loupekine snarks constructed from the Petersen Graph and verify Fulkerson’s Conjecture for this family. In addition, we show that the technique used in the proof can be applied to families constructed from snarks other than the Petersen Graph. As an example, we extend the main result to Loupekine snarks constructed from the generalised Blanuša snarks.