Fig. 4

Example of a scaffold graph produced by Construction 2. The input graph is composed by the edges \(e_1 = v_1v_2\), \(e_2 = v_2v_3\), \(e_3= v_1v_3\), \(e_4= v_1v_4\) and \(e_5 = v_3v_4\). Gray vertices in the figure belong to an edge gadget and white vertices belong to a vertex gadget. Matching edges are bold. Solid edges have weight zero and dashed edges have weight one. The long vertex-cycle \(C(v_2)\) corresponds to the vertices \(\{\overline{v}^2_1,v^2_1,u^2_2,\overline{u}^2_2,u^2_1,\overline{u}^2_1,v^2_2,\overline{v}^2_2\}\)