Oriented ribbon graphs (dessins d'enfant) are graphs embedded in oriented
surfaces. A quasi-tree of a ribbon graph is a spanning subgraph with one face,
which is described by an ordered chord diagram. We show that for any link
diagram L, there is an associated ribbon graph whose quasi-trees correspond
bijectively to spanning trees of the graph obtained by checkerboard coloring
L. This correspondence preserves the bigrading used for the spanning tree
model of Khovanov homology, whose Euler characteristic is the Jones polynomial
of L. Thus, Khovanov homology can be expressed in terms of ribbon graphs,
with generators given by ordered chord diagrams.Comment: 8 pages, 5 figure