Considering the problem of transporting n items across a river using a boat that can carry k items, where some pairs of items cannot be left together unsupervised. Let G be the simple graph whose vertices correspond to items, and whose edges join pairs of items that need supervision.

What's an example of a connected graph G with 5 vertices for which a boat of size Vc(G) suﬃces to transport the items? Where Vc(G) is the size of a minimum vertex cover of G.

What's an example of a connected graph G with 5 vertices for which a boat of size Vc(G)+1 is required to transport the items?