On Imp-Sets and Kernels by Monochromatic Paths of the Duplication

Abstract

In $[4]$ H. Galana-Sanchez introduced the concept of kernels by monochromatic paths which generalize the concept of kernels. In $[6]$ they proved the necessary and sufficient conditions for the existence of kernels by monochromatic paths of the duplication of a subset of vertices of a digraph, where a digraph is without monochromatic directed circuits. In this paper we study independent by monochromatic paths sets and kernels by monochromatic paths of the duplication. We generalize result from $[6]$ for an arbitrary edge coloured digraph.