A note on the \(P_3\)-isolation number of a graph
type: Item
instance of: scholarly article
title: A note on the \(P_3\)-isolation number of a graph
author: Xiaohua Wei
author: Gang Zhang
author: Biao Zhao
published in: RAIRO. Operations Research
publication date: 2025-01-08T00:00:00Z
review text: Let \(G\) be a graph, \(v\in V(G)\) and \(D\subseteq V(G)\). As usual, closed neighborhood \(N_G[v]\) contains \(v\) and all its neighbors and \(N_G[D]=\cup_{u\in D}N_G[u]\). A set \(D\) is called a \(P_3\)-isolating set if \(G-N_G[D]\) contains no path \(P_3\). The \(P_3\)-isolation number \(\iota(G,P_3)\) of \(G\) is the minimum cardinality of a \(P_3\)-isolating set.\N\NThe main result of the present contribution is that \(\iota(G,P_3)\leq \frac{n}{4}\) for a connected triangle-free and induced \(C_6\)-free graph \(G\notin\{P_3,C_3,C_6\}\) on \(n\) vertices. Moreover, this bound is sharp.
reviewed by: Iztok Peterin
Mathematics Subject Classification ID: 05C69
zbMATH DE Number: 7963468
zbMATH Keywords: isolation number
MaRDI profile type: Publication
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DOI: 10.1051/RO/2024178
description: scientific article; zbMATH DE number 7963468