Hasse diagram with maximal chain not counted in maximal anti-chain

Question

Construct a post (Hasse diagram) that contains a maximal anti-chain of size $r$ and, after removing a chain $C$ of maximal size, it still contains an anti-chain of size $r$.

Answer 1

Try this partial order; I’ll let you find the right maximal chain to remove.

        *     *  
         \   / \
          \ /   \
           *     *  
          / \   /  
         /   \ /  
        *     *  
         \   /  
          \ /  
           *