Abstract
For a given integer kge 1, a graph G with at least 2k vertices is called k-path-pairable, if for any set of k disjoint pairs of vertices, s_i,t_i, 1le ile k, there exist pairwise edge-disjoint s_i,t_i-paths in G. The path-pairability numberis the largest k such that G is k-path-pairable. Bounds on the path-pairability number are given here if G is the graph of infinite integer grids in the Euclidean plane. We prove that the path-pairability number of the integer quadrant is 4, and we show that the integer half-plane is 6-path-pairable and at most 7-path-pairable.
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