Bipartite Graphs and Matchings · Superchallenge problem

A graph has $11$ vertices and three $5$-cycles, all sharing the single common edge $1\text{-}2$: cycle $A = 1\text{-}2\text{-}3\text{-}4\text{-}5\text{-}1$, cycle $B = 1\text{-}2\text{-}6\text{-}7\text{-}8\text{-}1$, and cycle $C = 1\text{-}2\text{-}9\text{-}10\text{-}11\text{-}1$. What is the minimum number of edges that must be removed so the whole graph becomes bipartite?