@article {
author = {Galeana-Sánchez, Hortensia and Rojas-Monroy, Roc´ıo and Sanchez Lopez, Maria del Rocio and Zavala-Santana, Berta},
title = {$H$-kernels by walks in subdivision digraph},
journal = {Transactions on Combinatorics},
volume = {9},
number = {2},
pages = {61-75},
year = {2020},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2020.107875.1529},
abstract = {Let $H$ be a digraph possibly with loops and $D$ a digraph without loops whose arcs are colored with the vertices of $H$ ($D$ is said to be an $H$-colored digraph). A directed walk $W$ in $D$ is said to be an $H$-walk if and only if the consecutive colors encountered on $W$ form a directed walk in $H$. A subset $N$ of the vertices of $D$ is said to be an $H$-kernel by walks if (1) for every pair of different vertices in $N$ there is no $H$-walk between them ($N$ is $H$-independent by walks) and (2) for each vertex $u$ in $V$($D$)-$N$ there exists an $H$-walk from $u$ to $N$ in $D$ ($N$ is $H$-absorbent by walks). Suppose that $D$ is a digraph possibly infinite. In this paper we will work with the subdivision digraph $S_H$($D$) of $D$, where $S_H$($D$) is an $H$-colored digraph defined as follows: $V$($S_H$($D$)) = $V$($D$) $\cup$ $A$($D$) and $A$($S_H$($D$)) = \{($u$,$a$) : $a$ = ($u$,$v$) $\in$ $A$($D$)\} $\cup$ \{($a$,$v$) : $a$ = ($u$,$v$) $\in$ $A$($D$)\}, where ($u$, $a$, $v$) is an $H$-walk in $S_H$($D$) for every $a$ = ($u$,$v$) in $A$($D$). We will show sufficient conditions on $D$ and on $S_H$($D$) which guarantee the existence or uniqueness of $H$-kernels by walks in $S_H$($D$).},
keywords = {Kernel,Kernel by monochromatic paths,$H$-kernel by walks,subdivision digraph},
url = {http://toc.ui.ac.ir/article_24341.html},
eprint = {http://toc.ui.ac.ir/article_24341_2a0223bff824f193c06ca18595725ca4.pdf}
}