Bipartite Graphs and Matchings · Hard problem

A Mobius ladder $M_8$ has an outer $8$-cycle on vertices $0,1,\dots,7$ (edges $01,12,\dots,67,70$) together with $4$ "diameter" edges joining each vertex to the one directly opposite it: $04, 15, 26, 37$. What is the minimum number of edges that must be removed so the whole graph becomes bipartite?