On \((C_n;k)\) stable graphs
type: Item
instance of: scholarly article
title: On \((C_n;k)\) stable graphs
zbMATH Open document ID: 1229.05136
author: Sylwia Cichacz
author: Andrzej Żak
author: Agnieszka Görlich
author: Małgorzata Zwonek
published in: The Electronic Journal of Combinatorics
publication date: 2011-11-22T00:00:00Z
full work available at URL: v18i1p205.html
review text: Summary: A graph \(G\) is called \((H; k)\)-vertex stable if \(G\) contains a subgraph isomorphic to \(H\) ever after removing any \(k\) of its vertices; stab\((H; k)\) denotes the minimum size among the sizes of all \((H; k)\)-vertex stable graphs. In this paper we deal with \((C_n; k)\)- vertex stable graphs with minimum size. For each \(n\) we prove that stab\((C_n; 1)\) is one of only two possible values and we give the exact value for infinitely many \(n\)'s. Furthermore we establish an upper and lower bound for stab\((C_n; k)\) for \(k \geq 2\).
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 5976483
zbMATH Keywords: \((H
zbMATH Keywords: k)\)-vertex stable graph
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5976483