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A sufficient condition for graphs to be weakly $$k$$-linked. (English) Zbl 0780.05036
Let $$G=(V,E)$$ be a finite, undirected, loopless graph with vertex set $$V$$ and edge set $$E$$. For a natural number $$k$$, let $$g(k)$$ be the smallest natural number so that the following holds: Let $$G$$ be an $$n$$-edge- connected graph and let $$s_ 1,s_ 2,\dots,s_ k$$, $$t_ 1,t_ 2,\dots,t_ k$$ be vertices of $$G$$. Then for every $$i\in \{1,2,\dots,k\}$$ there exists a path $$P_ i$$ from $$s_ i$$ to $$t_ i$$ so that $$P_ 1,P_ 2,\dots,P_ k$$ are pairwise edge-disjoint.
The author proves that: $g(k)\leq\begin{cases} k+1, & \text{ if } k\text{ is odd},\\ k+2, &\text{ if } k\text{ is even}.\end{cases}$ .
Reviewer: L.Caccetta (Perth)

##### MSC:
 05C38 Paths and cycles
##### Keywords:
cut; linked graphs; edge-connected graph; path
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##### References:
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