A counterexample to the odd 2–factored snarks conjecture

A snark is a cubic cyclically 4–edge connected graph with edge chromatic number four and girth at least five. We say that a graph G is odd 2–factored if for each 2–factor F of G each cycle of F is odd. In this extended abstract, we present a method for constructing odd 2–factored snarks. In particular, we construct two families of odd 2–factored snarks of order 26 and 34 that disprove a previous conjecture by some of the authors.