Graph Coloring · Hard problem

The wheel $W_7$ has a hub vertex joined to all $7$ rim vertices of the $7$-cycle $1\text{-}2\text{-}3\text{-}4\text{-}5\text{-}6\text{-}7\text{-}1$ ($14$ edges in all). What is the minimum number of RIM edges that must be deleted so that the graph left behind can be properly colored with only $3$ colors?