In the paper "Stable dominating circuits in snarks" (Discrete Math 233 (247-256) 2001) Martin Kochhol gives a counter example to this conjecture (in fact he gives an infinite family of them).
Using computer search I have found even smaller counter examples (the smallest has just 20 vertices).
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CSI of Charles University
This conjecture is false
In the paper "Stable dominating circuits in snarks" (Discrete Math 233 (247-256) 2001) Martin Kochhol gives a counter example to this conjecture (in fact he gives an infinite family of them).
Using computer search I have found even smaller counter examples (the smallest has just 20 vertices).
Best regards,
Jonas Hägglund