. Also, note that for all i, ?(u, v, x i , y i ) = d(x i , y i )/2 and so, we have that for every i: d(x i , y i ) ? 2?

. Proof, We proceed by contradiction Let us assume that one of the graphs of Figure 1 is an isometric subgraph of G. For each of the forbidden graphs of Condition 5, we will only consider the 4-tuple of vertices that are drawn in bold in Figure 1

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