Kernels in circulant digraphs

A kernel J of a digraph D is an independent set of vertices of D such that for every vertex w ∈ V (D) ∖ J there exists an arc from w to a vertex in J. In this paper, among other results, a characterization of 2 -regular circulant digraph having a kernel is obtained. This characterization is a partial solution to the following problem: Characterize circulant digraphs which have kernels; it appeared in the book Digraphs - theory, algorithms and applications, Second Edition, Springer-Verlag, 2009, by J. Bang-Jensen and G. Gutin.