A Turaev surface approach to Khovanov homology
  We introduce Khovanov homology for ribbon graphs and show that the Khovanov homology of a certain ribbon graph embedded on the Turaev surface of a link is isomorphic to the Khovanov homology of the link (after a grading shift). We also present a spanning quasi-tree model for the Khovanov homology of a ribbon graph. 
Oliver T. Dasbach and Adam M. Lowrance
math.GT