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We construct for all $k\in \mathbb{N}$ a $k$-edge-connected digraph $D$ with $x_1,y_1,x_2,y_2\in V(D)$ such that there are no edge-disjoint $x_1 \rightarrow y_1$ and $x_2\rightarrow y_2$ paths. We also prove that contrary to the directed case, for undirected graphs, $(2n-1)$-edge-connectivity implies the linkability of arbitrary $n$ terminal pairs with edge-disjoint paths.
Bibtex entry:
| AUTHOR | = | {Jo{\'o}, Attila}, |
| TITLE | = | {Edge-Disjoint Paths Problem in Highly Connected, Infinite Graphs}, |
| NOTE | = | {{\tt www.cs.elte.hu/egres}}, |
| INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
| YEAR | = | {2014}, |
| NUMBER | = | {TR-2014-10} |