$H$-kernels in the $D$-join

Abstract

In $[8]$ the concept of $H$-kernel was introduced, which generalizes the concepts of kernel and kernel by monochromatic paths. In this paper, we prove necessary and sufficient conditions for the existence of H-kernels in the $D$-join of digraphs, and consequently, we will give a sufficient condition for the $D$-join to be $H$-kernel perfect.