Algebraic and geometric aspects of bipartite planar graphs
  Let B_{2t} be a bipartite planar graph with an even number of regions. We are able to find bounds for the graded Betti numbers and the projective dimension of the quotient ring associated to the graph. We also will investigate the minimal vertex covers and the maximum matchings related to such a graph. 
Maurizio Imbesi and Monica La Barbiera
math.AC