Bipartite Graphs and Matchings · Challenge problem

A network has two separate pieces with no links between them: a $4$-cycle $1\text{-}2\text{-}3\text{-}4\text{-}1$, and a second, separate $4$-cycle $5\text{-}6\text{-}7\text{-}8\text{-}5$. How many different MINIMUM vertex covers does the whole network have?