H-Kernels by Walks

TL;DR

This paper proves that in a directed graph where every cycle is an $H$-cycle, an $H$-kernel by walks always exists, extending the understanding of kernel existence conditions.

Contribution

It establishes a new sufficient condition for the existence of $H$-kernels by walks based on cycle properties.

Findings

If every cycle of $D$ is an $H$-cycle, then $D$ has an $H$-kernel by walks.

Provides a theoretical proof for the existence of $H$-kernels under specific cycle conditions.

Enhances the theory of kernels in directed graphs with respect to $H$-cycles.

Abstract

We prove that, if every cycle of $D$ is an $H$-cycle, then $D$ has an $H$-kernel by walks.