  Among all torus links, we characterise those arising as links of simple plane
curve singularities by the property that their fibre surfaces admit only a
finite number of cutting arcs that preserve fibredness. The same property
allows a characterisation of Coxeter-Dynkin trees (i.e., $A_n$, $D_n$, $E_6$,
$E_7$ and $E_8$) among all positive tree-like Hopf plumbings.
