On finding convex cuts in general, bipartite and plane graphs

Our method for characterizing and finding convex cuts of a connected plane graph G is motivated by the concept of alternating cuts and conditions on the latter to be convex. In the last part of this paper we represent alternating cuts as plane curves and focus on their intersection pattern. If the plane curves form an arrangement of pseudolines, G is scale embedded in its dual, and any edge of G is contained in the cut-set of a convex cut of G.