?. , ?V (F h ) by setting ? (z) = ? (z) for z ? Z. Since ? is an injection, ? is also an injection. Because F is 2-connected, ? satisfies (i) and (ii), Let ? : V (H) ? V (G) be an injection that extends ? such that F = G? ? H is 2-connected. We define ? : Z ? (V (F 0 )\?(X ?Y ))?V (F 1 )

.. .. , p s ) = +?. It implies that there is no injection ?

, We use dynamic programming to compute ? h consequently for h = 0, 1,. .. , r. We start with computing ? 0 (q 1 ,. .. , q s ) for each s-tuple (q 1 ,. .. , q s ). Notice that the conditions (a) and (b) are irrelevant in this case, because they concern only h ? 1. We construct the auxiliary complete bipartite graph G 0 with the bipartition (V (F 0 ) \ ?(X ? Y ), Z ) of its vertex set and define the weight of each edge zv for z ? Z and v ? V (F 0 ) \ ?(X?Y ) as w(z, v), ? V (F h ) satisfying (a) and (b). But this immediately implies that there is no injective extension ? of ? satisfying (i) and (ii)

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