On the diagonal queens domination problem
type: Item
instance of: scholarly article
title: On the diagonal queens domination problem
zbMATH Open document ID: 0589.05014
DOI: 10.1016/0097-3165(86)90012-9
author: E. J. Cockayne
author: Stephen T. Hedetniemi
published in: Journal of Combinatorial Theory. Series A
publication date: 1986-01-01T00:00:00Z
review text: Let the squares of an \(n\times n\) chessboard be labelled (i,j), so that black and white squares have \(i+j\) even and odd, respectively. A subset K of \(N=\{1,...,n\}\) is a diagonal dominating set if queens placed in positions \(\{\) (k,k): \(k\in K\}\) dominate the entire board. A subset X of N is called midpoint-free if for all (i,j)\(\subseteq X\), \((i+j)/2\not\in X\), and X is an even-sum subset if its elements are either all odd or all even. It is shown that K is a diagonal dominating set if and only if N-K is a midpoint-free, even-sum set. If diag (n)\(=\min \{| K|:\) K is a diagonal dominating set\(\}\) and \(r_ 3(n)\) is the smallest k such that any k-subset of N contains a 3-term arithmetic progression, then diag (n)\(=n+1-r_ 3([n/2])\).
reviewed by: Betty Garrison
Mathematics Subject Classification ID: 05A99
Mathematics Subject Classification ID: 11B25
zbMATH DE Number: 3946141
zbMATH Keywords: chessboard
zbMATH Keywords: diagonal dominating set
zbMATH Keywords: midpoint-free
zbMATH Keywords: even-sum subset
zbMATH Keywords: arithmetic progression
MaRDI profile type: Publication
full work available at URL: 0097-3165(86)90012-9
OpenAlex ID: W2065090732
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description: scientific article; zbMATH DE number 3946141