Odd 2-factored snarks
  A {\em 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 {\em odd 2-factored} if for each 2-factor F of G each cycle of F is odd.   In this paper, we present a method for constructing odd 2--factored snarks. In particular, we construct two families of odd 2-factored snarks that disprove a conjecture by some of the authors. Moreover, we approach the problem of characterizing odd 2-factored snarks furnishing a partial characterization of cyclically 4-edge connected odd 2-factored snarks. Finally, we pose a new conjecture regarding odd 2-factored snarks. 
M.Abreu, D.Labbate, R.Rizzi, J.Sheehan
math.CO cs.DM