English

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 44-quasi-transitive and 44-transitive digraphs, as well as 22-anti-transitive, and asymmetrical 44-anti-transitive digraphs with bounded diameter, which are critical kernel imperfect.

Keywords

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}
}

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20 pages