Paired domination in graphs with minimum degree four

Fuente: arXiv
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Main Authors: Bujtás, Csilla, Henning, Michael A.
Format: Preprint
Published: 2025
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author Bujtás, Csilla
Henning, Michael A.
author_facet Bujtás, Csilla
Henning, Michael A.
contents A set $S$ of vertices in a graph $G$ is a paired dominating set if every vertex of $G$ is adjacent to a vertex in $S$ and the subgraph induced by $S$ admits a perfect matching. The minimum cardinality of a paired dominating set of $G$ is the paired domination number $\gpr(G)$ of $G$. We show that if $G$ is a graph of order~$n$ and $δ(G) \ge 4$, then $\gpr(G) \le \frac{10}{17}n < 0.5883 n$.
format Preprint
id arxiv_https___arxiv_org_abs_2505_01815
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Paired domination in graphs with minimum degree four
Bujtás, Csilla
Henning, Michael A.
Combinatorics
05C69
A set $S$ of vertices in a graph $G$ is a paired dominating set if every vertex of $G$ is adjacent to a vertex in $S$ and the subgraph induced by $S$ admits a perfect matching. The minimum cardinality of a paired dominating set of $G$ is the paired domination number $\gpr(G)$ of $G$. We show that if $G$ is a graph of order~$n$ and $δ(G) \ge 4$, then $\gpr(G) \le \frac{10}{17}n < 0.5883 n$.
title Paired domination in graphs with minimum degree four
topic Combinatorics
05C69
url https://arxiv.org/abs/2505.01815