At least three minimal quasi-kernels
If D D is a digraph, then K?V(D) K ? V ( D ) is a quasi-kernel of D D if K K is independent and for each y?V(D)?K y ? V ( D ) ? K there is x?K x ? K such that the directed distance from y y to x x is less than three. Note that any independent superset of a quasi-kernel is a quasi-kernel. Jacob and Meyniel have given a sufficient condition for a digraph to have at least three quasi-kernels, however these quasi-kernels need not be minimal. We give sufficient conditions for a digraph to have at least three minimal quasi-kernels.
minimal quasi-kernel quasi-kernel