  Cerium is a fascinating element exhibiting, with its different phases,
long-range magnetic order and superconductivity in bulk form. The coupling of
the 4f electron to sd conduction electrons and to the lattice is responsible
for unique structural and electronic properties like the isostructural
first-order solid-solid transition from the cubic $\gamma$ phase to the cubic
$\alpha$ phase, which is accompanied by a huge volume collapse of 14 %. While
the $\gamma - \alpha$ phase transition has been investigated for decades,
experiments aiming at disentangling the 4f contribution to the electric
conductance of the different phases have not been performed. Here we report on
the strongly enhanced conductance of single-atom Ce contacts. By controlling
the content of $\alpha$-Ce employing different rates of cooling, we find a
strong correlation between the fraction of $\alpha$-Ce and the magnitude of the
last conductance plateau before the contact breaks. We attribute the enhanced
conductance of $\alpha$-Ce to the additional contribution of the 4f level.
