Let G = (V, E) be an undirected unweighted graph on n vertices. A subgraph H of G is called an (all-pairs) purely additive spanner with stretch β if for every (u, v) The problem of computing sparse spanners with small stretch β is well-studied. Here we consider the following relaxation: we are given P ⊆ V ×V and we seek a sparse subgraph Such a subgraph is called a pairwise spanner with additive stretch β and our goal is to construct such subgraphs that are sparser than all-pairs spanners with

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... he same stretch. We show sparse pairwise spanners with additive stretch 4 and with additive stretch 6. We also consider the following special cases: P = S × V and P = S × T , where S ⊆ V and T ⊆ V , and show sparser pairwise spanners for these cases.