Abstract
A graph G is called n-geodetically edge-connected if the removal of any n-1 edges does not increase the distance between any pair of non-adjacent vertices. We prove that if G is n-geodetically edge-connected, n≠2, then for any 2n pairwise distinct vertices s1,t1,...,sn,tn there are n pairwise edge-disjoint paths P1,...,Pn such that Pi connects si and ti and the length of Pi equals the distance of si and ti for 1≤i≤n. We also give a solution for n=2. Moreover, we present for each nε IN a polynomial algorithm that takes a n-geodetically edge-connected graph and the vertices s1,t1,...,sn,tn as input and determines n shortest edge-disjoint paths as mentioned.
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© 1989 Springer-Verlag Berlin Heidelberg
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Schwill, A. (1989). Shortest edge-disjoint paths in graphs. In: Monien, B., Cori, R. (eds) STACS 89. STACS 1989. Lecture Notes in Computer Science, vol 349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029011
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DOI: https://doi.org/10.1007/BFb0029011
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