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The conjecture of Beineke and Harary states that for any two vertices which can be separated by $k$ vertices and $l$ edges for $l\geq 1$ but neither by $k$ vertices and $l-1$ edges nor $k-1$ vertices and $l$ edges there are $k+l$ edge-disjoint paths connecting these two vertices of which $k+1$ are internally disjoint. In this paper we consider this conjecture for $l=2$ and any $k\in \mathbb{N}$... (read more)
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