Simple enumeration of minimal cutsets separating 2 vertices in a class of undirected planar graphs

The problem of enumerating all the s-t minimal cutsets separating two vertices s and t specified in a class of undirected planar graphs, called D-S (delta-star) reducible graphs, is presented. The problem is handled by a new enumeration approach based on graph reductions that preserve minimal cutsets such that a graph with complex structure is transformed into a single edge connecting s and t by recursive applications. Some classes of undirected planar graphs, such as series-parallel and wheel graphs, are identified to be D-S reducible. The approach is provided with a polynomial-time (measured in total number of vertices) enumeration algorithm which is illustrated with a numerical example. The efficiency is shown through some computational experience