Fig. 5

The solution S is composed of a single alternating path \(\{v_1,\dots ,v_6\}\). S is closeable by subgraph \(G_3= \{x_3,y_3\}\): we can close the alternating path of S into an alternating cycle by adding the edges \(v_1x_3\), \(x_3y_3\) and \(y_3v_6\). S is extensible by subgraph \(G_2 = \{x_2,y_2\}\): we can extend the alternating path of S by adding the edges \(v_6y_2\) and \(y_2x_2\) without changing the number of paths in S. S is absorbent to \(G_4 = \{x_4,y_4\}\): we can replace the edge \(v_2v_3\) of S by the edges \(v_2y_4,y_4x_4\) and \(x_4v_3\) without changing the number of paths in S. S is frozen to \(G_1= \{x_1,y_1\}\)