Disjoint shortest paths in graphs


It is an interesting problem that how much connectivity ensures the existence ofn disjoint paths joining givenn pairs of vertices, but to get a sharp bound seems to be very difficult. In this paper, we study how muchgeodetic connectivity ensures the existence ofn disjointgeodesics joining givenn pairs of vertices, where a graph is calledk-geodetically connected if the removal of anyk−1 vertices does not change the distance between any remaining vertices.

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Enomoto, H., Saito, A. Disjoint shortest paths in graphs. Combinatorica 4, 275–279 (1984). https://doi.org/10.1007/BF02579137

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AMS subject classification (1980)

  • 05 C 40
  • 05 C 38