An upper bound for the minimum number of queens covering the \(n {\times} n\) chessboard
type: Item
instance of: scholarly article
title: An upper bound for the minimum number of queens covering the \(n {\times} n\) chessboard
zbMATH Open document ID: 0993.05105
DOI: 10.1016/S0166-218X(01)00244-X
published in: Discrete Applied Mathematics
publication date: 2002-08-29T00:00:00Z
review text: A set of queens on an \(n\times n\) chessboard \(Q_n\) dominates the chessboard if every field is either occupied or attacked by a queen. It is an old problem to determine the exact value of the minimum number \(\gamma(Q_n)\) of queens needed to dominate \(Q_n\). Using explicit constructions the authors prove that \(\gamma(Q_n)\leq \frac{8}{15}n+O(1)\) which considerably narrows the gap between the best known lower bound (essentially due to Spencer) and the previously known best upper bound due to the same authors and Cockayne.
reviewed by: Dieter Rautenbach
Mathematics Subject Classification ID: 05C69
zbMATH DE Number: 1792332
zbMATH Keywords: queen
zbMATH Keywords: chessboard
zbMATH Keywords: domination
author: A. P. Burger
author: Christina M. Mynhardt
MaRDI profile type: Publication
cites work: Q3277097
cites work: Q4309111
cites work: Domination and irredundance in the queens' graph
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cites work: Q3139865
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full work available at URL: s0166-218x(01)00244-x
OpenAlex ID: W2040300226
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description: scientific article; zbMATH DE number 1792332