It could only be possible to cut every edge if the graph is bipartite (the cut itself would give the vertex bipartition). The given example is not a bipartite graph (e.g. it contains a $K_3$).
It could only be possible to cut every edge if the graph is bipartite (the cut itself would give the vertex bipartition). The given example is not a bipartite graph (e.g. it contains a $K_3$).