Fractional Kernels in Digraphs

We define a fractional version of the notion of “kernels” in digraphs and prove that every clique–acyclic digraph (i.e., one in which no clique contains a cycle) has a fractional kernel. Using this we give a short proof of a recent result of Boros and Gurvich (proving a conjecture of Berge and Duchet) that every clique–acyclic orientation of a perfect graph has a kernel.