On kernel-less clique-acyclic orientations of minimally imperfect graphs Original Research Article

In this paper we will show some properties of the kernel-less clique-acyclic orientations of minimally imperfect graphs and discuss some relation between these properties, Berge and Duchetʹs Conjecture about kernel-solvability and the Strong Perfect Graph Conjecture. Especially, we will give a new equivalent formalization of the SPGC by using the concept unique fractional kernel.