Critical Kernel Imperfectness in $4$-quasi-transitive and $4$-anti-transitive digraphs of small diameter
Combinatorics
2024-05-06 v1
Abstract
A kernel in a digraph is an independent and absorbent subset of its vertex set. A digraph is critical kernel imperfect if it does not have a kernel, but every proper induced subdigraph does. In this article, we characterize asymmetrical -quasi-transitive and -transitive digraphs, as well as -anti-transitive, and asymmetrical -anti-transitive digraphs with bounded diameter, which are critical kernel imperfect.
Cite
@article{arxiv.2405.01767,
title = {Critical Kernel Imperfectness in $4$-quasi-transitive and $4$-anti-transitive digraphs of small diameter},
author = {Germán Benítez-Bobadilla and Hortensia Galeana-Sánchez and César Hernández-Cruz},
journal= {arXiv preprint arXiv:2405.01767},
year = {2024}
}
Comments
20 pages