The maximum corank of graphs with a 2-separation Original Research Article

For a graph G=(V,E) with vertex-set V={1,2,…,n}, which is allowed to have parallel edges, and for a field F, let image be the set of all F-valued symmetric n×n matrices A which represent G. The maximum corank of a graph G is the maximum possible corank over all image. If (G1,G2) is a (less-than-or-equals, slant2)-separation, we give a formula which relates the maximum corank of G to the maximum corank of some small variations of G1 and G2.