Edge-Disjoint Linkage in Infinite Graphs

Amena Assem (York University)

In 1980 Thomassen conjectured that, for odd \(k\), every \(k\)-edge-connected graph (finite or infinite) is weakly \(k\)-linked. The conjecture is still open, however, in 1991, Huck proved that an edge-connectivity of \(k+1\) is sufficient in the case of finite graphs. We prove that Huck’s result extends to all infinite graphs, thus improving a result of Ok, Richter, and Thomassen from 2016 where they showed that \((k+2)\)-edge-connectivity implies weak \(k\)-linkedness for \(1\)-ended locally finite graphs. This is joint work with Bruce Richter.

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