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:
@techreport{egres-14-10,
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} |